Pipes & Cisterns

PrepBank · পাতা ২ / ৫ · ১০১–২০০ / ৪০৮

১০১.

An ingoing pipe was used to fill a tank. But while using an outgoing pipe that can pour water in 10 hours at the same time, it took 8 hours to fill the tank. The ingoing pipe can fill the tank alone in -

ক
30/9 hours
খ
40/11 hours
গ
20/3 hours
ঘ
40/9 hours

ব্যাখ্যা

Question: An ingoing pipe was used to fill a tank. But while using an outgoing pipe that can pour water in 10 hours at the same time, it took 8 hours to fill the tank. The ingoing pipe can fill the tank alone in -

Solution:
Let,
the ingoing pipe can fill the tank in X hours.
so, total fill-up in one hour = 1/X - 1/10
= (10 - X)/10X
ATQ,
10X/(10 - X) = 8
10X = 80 - 8X
18X = 80
X = 80/18 = 40/9 hours

১০২.

A tap can fill a cistern in 8 hours. Due to a drain pipe in the bottom, it takes 10 hours to fill the same cistern. If the cistern is full, how much time will the drain pipe take to empty it?

ক
21 hours
খ
27 hours
গ
35 hours
ঘ
40 hours

ব্যাখ্যা

Question: A tap can fill a cistern in 8 hours. Due to a drain pipe in the bottom, it takes 10 hours to fill the same cistern. If the cistern is full, how much time will the drain pipe take to empty it?

সমাধান:
ট্যাপ দ্বারা 1 ঘন্টায় পূর্ণ হয় 1/8 অংশ।
নল ও ছিদ্র দ্বারা একত্রে 1 ঘন্টায় পূর্ণ হয় 1/10 অংশ।

∴ ছিদ্র দ্বারা 1 ঘন্টায় খালি হয় = (ট্যাপের কাজ - যৌথ কাজ)
= (1/8 - 1/10) অংশ
= (5 - 4)/40 অংশ
= 1/40 অংশ।

∴ ছিদ্রটি সম্পূর্ণ চৌবাচ্চাটি খালি করতে 40 ঘন্টা সময় নেবে।

১০৩.

Tap B is 5 times slower than Tap A in filling the same tank. Also tap B takes 32 minutes more than Tap A to fill the same tank completely. How long will the tank take to get full, if both the taps are opened simultaneously?

ক
ক) 20/3 hours
খ
খ) 22/3 hours
গ
গ) 25/3 hours
ঘ
ঘ) 29/3 hours

ব্যাখ্যা

Let Tap A take T minutes to fill the tank alone.
Since Tap A is 5 times faster than Tap B, Tap B takes 5 times more time.
So time taken by Tap B = 5T minutes
Also, 5T-T = 32 ----------- Given
∴ T = 8 minutes = Time taken by A
Time taken by B = 5 x 8 = 40 minutes.

In 1 min, A + B fills = 1/8 + 1/40 = 3/20 parts
So entire tank is filled in = 20/3 hours.

১০৪.

A pipe can fill up an empty tank in 12 minutes, Another pipe flows out 8 liters of water per minute. If the two pipes are opened together and the empty tank is filled up in 84 minute. How much water does the tank contain?

ক
ক) 92 liter
খ
খ) 105 liter
গ
গ) 112 liter
ঘ
ঘ) 120 liter

ব্যাখ্যা

Question: A pipe can fill up an empty tank in 12 minutes, Another pipe flows out 8 liters of water per minute. If the two pipes are opened together and the empty tank is filled up in 84 minutes. How much water does the tank contain?

Solution:
Let the tank empty in x minute

According to the question,
(1/12) - (1/x) = 1/84
⇒ (1/12) - (1/84) = 1/x
⇒ 6/84 = 1/x
⇒ x = 84/6
⇒ x = 14

The tank emptied by the other pipe in 14 minute

∴ The tank contain = 14 × 8 = 112 liter

১০৫.

3/7 part of the tank is full of water. When 42 liters of water is taken out, the tank becomes empty. The capacity of the tank is -

ক
82 liters
খ
66 liters
গ
78 liters
ঘ
98 liters

ব্যাখ্যা

Question: 3/7 part of the tank is full of water. When 42 liters of water is taken out, the tank becomes empty. The capacity of the tank is -

Solution:
Let us consider,
The tank has 7x liters of total capacity and holds 3x litres of water.
And if 42 liters of water is taken out, then the tank becomes empty.

It means 3x litres of water is taken out.
∴ 3x = 42 liters
⇒ x = 14 liters

∴ Capacity of tank = 7x = 7 × 14 = 98 liters

১০৬.

Three pipes A, B, and C would fill a tank in 10 hours, 15 hours, and 20 hours respectively. If all these pipes are opened simultaneously, how much time will be taken to fill the tank?

ক
ক) 5 hr.
খ
খ) 60/13 hr.
গ
গ) 50/13 hr.
ঘ
ঘ) 6 hr.

ব্যাখ্যা

Question: Three pipes A, B, and C would fill a tank in 10 hours, 15 hours, and 20 hours respectively. If all these pipes are opened simultaneously, how much time will be taken to fill the tank?

Solution:
A, 1 ঘন্টায় পূর্ণ করে (1/10) অংশ
B, 1 ঘন্টায় পূর্ণ করে (1/15) অংশ
C, 1 ঘন্টায় পূর্ণ করে (1/20) অংশ

তিনটি পাইপ একত্রে পূর্ণ করে = (1/10) + (1/15) + (1/20) = 13/60 অংশ

আবার,
13/60 অংশ পূর্ণ করে 1 ঘণ্টায়
∴ 1 অংশ পূর্ণ করে 60/13 ঘণ্টায়

১০৭.

Pipes A and B can fill a tank in 15 hours and 20 hours respectively and pipe C can empty the full tank in 30 hours. If all the pipes are opened together, how much time will be needed to make the tank full?

ক
ক) 8 hours
খ
খ) 10 hours
গ
গ) 12 hours
ঘ
ঘ) 14 hours

ব্যাখ্যা

Time taken by pipe A to fill the tank =15 hours
Portion of tank filled by pipe A in 1 hour =1/15

Time taken by pipe B to fill the tank =20 hours
Portion of Tank filled by pipe B in 1 hour 1/20

Time taken by pipe C to empty the tank =30 hours
Portion of tank emptied by pipe C in 1 hour 1/30

Now, Portion of tank filled by all three pipes together in 1 hour
=1/15 + 1/20 - 1/30
= (4 + 3 - 2)/60
= 5/60
= 1/12

Time taken to filled the tank when all three pipes are opened together = 12 hours

১০৮.

Time required by two pipes A and B working separately to fill a tank is 36 seconds and 45 seconds respectively. Another pipe C can empty the tank in 30 seconds. Initially, A and B are opened and after 7 seconds, C is also opened. In how much more time the tank would be completely filled?

ক
43 seconds
খ
35 seconds
গ
47 seconds
ঘ
39 seconds

ব্যাখ্যা

Question: Time required by two pipes A and B working separately to fill a tank is 36 seconds and 45 seconds respectively. Another pipe C can empty the tank in 30 seconds. Initially, A and B are opened and after 7 seconds, C is also opened. In how much more time the tank would be completely filled?

Solution:
Let the capacity of the tank be LCM (36, 45, 30) = 180 units
∴ Efficiency of pipe A = 180/36 = 5 units/second
Efficiency of pipe B = 180/45 = 4 units/second
Efficiency of pipe C = - 180 / 30 = - 6 units/second

Now,
for the first 7 seconds, A and B were open.
Combined efficiency of A and B = 5 + 4 = 9 units/second
∴ Part of the tank filled in 7 seconds = 7 × 9 = 63 units

Part of tank empty = 180 - 63 = 117 units

Now, all pipes are opened.
Combined efficiency of all pipes = 5 + 4 - 6 = 3 units/second
Therefore, more time required = 117/3 = 39 seconds.

১০৯.

Two pipes together can fill a tank in 6 hours. One pipe alone can do it in 12 hours. Another pipe alone can fill two tanks in -

ক
24 hours
খ
18 hours
গ
36 hours
ঘ
30 hours

ব্যাখ্যা

Question: Two pipes together can fill a tank in 6 hours. One pipe alone can do it in 12 hours. Another pipe alone can fill two tanks in -

Solution:
let the second pipe fill the tank in X hours.

in one hour both pipes can fill = 1/12 + 1/X
= (X + 12)/12X

Atq,
12X/(X + 12) = 6
x = 12 hours.

to fill two tanks it will take = 24 hours

১১০.

A tank can be filled by a tap in 20 minutes and by another tap in 60minutes. Both the taps are kept open for 10 minutes and the first tap is shut off. After this, the tank will be completely filled what time?

ক
ক) 10 minutes
খ
খ) 15 minutes
গ
গ) 30 minutes
ঘ
ঘ) 20 minutes

ব্যাখ্যা

Question: A tank can be filled by a tap in 20 minutes and by another tap in 60minutes. Both the taps are kept open for 10 minutes and the first tap is shut off. After this, the tank will be completely filled what time?

Solution:
Part of the tank filled by both the taps in 1 minutes = (1/20) + (1/60) = (3 + 1)/60 = 1/15
Part of the tank filled by both the taps in 10 minutes =10(1/15) = 2/3
Remaining part =1- (2/3) =1/3

1/60 part of the tank is filled by the second pipe in 1 min.
∴1/3 of the tank will be filled by the second pipe in (60 × 1)/3= 20 min.

১১১.

A cistern is normally filled with water in 10 hours but takes 5 hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty the cistern in.

ক
ক) 24 hours
খ
খ) 30 hours
গ
গ) 40 hours
ঘ
ঘ) 50 hours

ব্যাখ্যা

1 ঘণ্টায় পানি ভর্তি হয় ট্যাংকের 1/10 অংশ
কিন্তু ছিদ্র থাকায় 1 ঘন্টায় পানি ভর্তি হয় ট্যাংকের 1/15 অংশ
1 ঘণ্টায় খালি হয় = (1/10 - 1/15) অংশ
= (3 - 2)/30 অংশ
= 1/30 অংশ

ছিদ্র দ্বারা 1/30 অংশ খালি হয় = 1 ঘণ্টায়
ছিদ্র দ্বারা 1 বা সম্পূর্ণ অংশ খালি হয় = (1 × 30)/1 = 30 ঘণ্টায়

১১২.

A tank is filled in 8 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

ক
36 hours
খ
48 hours
গ
56 hours
ঘ
64 hours

ব্যাখ্যা

Question: A tank is filled in 8 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Solution:
Let,
C can fill the tank in X hours
∴ B can do it in 2X hours and,
A can do it in 4X hours.

in one hour all the pipes can fill = (1/X + 1/2X + 1/4X)
= 7/4X

ATQ.
4X/7 = 8
X = 56/4
= 14
∴ time required for A is = 4 × 14 = 56 hours

১১৩.

A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time as the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is-

ক
3 hours
খ
6 hours
গ
9 hours
ঘ
15 hours
ঙ
None of the above

ব্যাখ্যা

Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time as the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is-

Solution:
Let the time taken by the first pipe = x hours

Then,
The second pipe fills the tank 5 hours faster than the first pipe
∴ Time = x - 5 hours
The third pipe fills the tank 4 hours faster than the second pipe
∴ Time = (x - 5) - 4 = x - 9 hours

ATQ,
(1/x) + {1/(x - 5)} = 1/(x - 9)
⇒ (x - 5 + x)/{x(x - 5)} = 1/(x - 9)
⇒ (2x - 5)(x - 9) = x(x - 5)
⇒ 2x² - 23x + 45 = x² - 5x
⇒ x² - 18x + 45 = 0
⇒ x² - 15x - 3x + 45 = 0
⇒ (x - 3)(x - 15) = 0
∴ x = 3 or x = 15
Since time cannot be less than 9 hours
Hence, x = 15

১১৪.

After filling half of a tank with an ingoing pipe that can fill the tank in 8 hours, an outgoing pipe was attached to empty the tank in 10 hours. How much time will it take to fill the whole tank?

ক
16 hours
খ
24 hours.
গ
26 hours.
ঘ
32 hours.

ব্যাখ্যা

Question: After filling half of a tank with an ingoing pipe that can fill the tank in 8 hours, an outgoing pipe was attached to empty the tank in 10 hours. How much time will it take to fill the whole tank?

Solution:
after 4 hours, the tank will be filled in half.
in one hour,
ingoing can fill = 1/8
outgoing can pour = 1/10
total fill-up in one hour = 1/8 - 1/10
= 1/40
∴ to fill te full tank it will take 40 hours.
so, half of the tank will take 20 hours.

total time to fill the tank from the beginning is = 4 + 20 = 24 hours.

১১৫.

A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water of the tank in:

ক
ক) 10 hours
খ
খ) 12 hours
গ
গ) 14 hours
ঘ
ঘ) 15 hours

ব্যাখ্যা

Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water of the tank in:

Solution:
Work done by the leak in 1 hour
= 1/2 - 3/7
= 1/14

∴ The leak will empty the tank in 14 hours

১১৬.

One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 24 minutes, then the slower pipe alone will be able to fill the tank in-

ক
5 hours
খ
4 hours
গ
3 hours
ঘ
2 hours

ব্যাখ্যা

Question: One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 24 minutes, then the slower pipe alone will be able to fill the tank in-

Solution:
Let,
the slower pipe alone fill the tank in x minutes.
Then, Faster pipe alone will fill it in x/4 minutes.

ATQ,
(1/x) + (4/x) = 1/24
⇒ 5/x = 1/24
∴ x = 120

∴ The slower pipe alone fill the tank in 120 minutes
= (120/60) hours
= 2 hours

১১৭.

An outlet pipe can empty a cistern in 3 hours. In what time will it empty 2/3 part of the cistern?

ক
2 hours
খ
3 hours
গ
4 hours
ঘ
5 hours

ব্যাখ্যা

Question: An outlet pipe can empty a cistern in 3 hours. In what time will it empty 2/3 part of the cistern?

Solution:
সম্পূর্ণ অংশ খালি করতে সময় লাগে ৩ ঘণ্টা
২/৩ অংশ খালি করতে সময় লাগে ৩ × ২/৩ ঘণ্টা
= ২ ঘণ্টা

১১৮.

Two pipes, Pipe X and Pipe Y, can fill a tank in 15 minutes and 30 minutes, respectively. If both pipes are opened together, how long will it take to fill the tank?

ক
16 minutes
খ
5 minutes
গ
18 minutes
ঘ
12 minutes
ঙ
10 minutes

ব্যাখ্যা

Question: Two pipes, Pipe X and Pipe Y, can fill a tank in 15 minutes and 30 minutes, respectively. If both pipes are opened together, how long will it take to fill the tank?

Solution:
pipe X fill a tank in 15 minutes so, it fills in one minute (1/15)
pipe Y fill a tank in 30 minutes so, it fills in one minute (1/30)

∴ Both pipes fill in one minute = (1/15) + (1/30) = (2 + 1)/30 = 3/30 = 1/10

so, it will take 1/(1/10) or 10 minutes to fill the tank.

১১৯.

Two pipes A and B can fill a cistern in 36 and 54 minutes respectively. Both pipes are opened together, after how many minutes should B be turned off, so that the cistern be fill in 24 minutes?

ক
21 minutes
খ
16 minutes
গ
18 minutes
ঘ
24 minutes

ব্যাখ্যা

Question: Two pipes A and B can fill a cistern in 36 and 54 minutes respectively. Both pipes are opened together, after how many minutes should B be turned off, so that the cistern be fill in 24 minutes?

Solution:
A can fill the cistern in 36 minutes
So in 1 min A can fill the cistern = 1/36 th part
In 24 min, A can fill the cistern = 24/36 = 2/3 rd

∴ Remaining part = 1 - (2/3) = 1/3 rd

As B can fill full cistern in 54 minutes
So it will fill 1/3 rd part in = (1/3) × 54) = 18 minutes.

১২০.

Working alone, two pipes A and B require 9 hours and 6.25 hours more respectively to fill a pool than if they were working together. Find the total time taken to fill the pool if both were working together.

ক
6 hours
খ
6.5 hours
গ
7 hours
ঘ
7.5 hours
ঙ
None of these

ব্যাখ্যা

Question: Working alone, two pipes A and B require 9 hours and 6.25 hours more respectively to fill a pool than if they were working together. Find the total time taken to fill the pool if both were working together.

Solution:
Let the time taken if both were working together be 'n' hours.
Time taken by A = n + 9
Time taken by B = n + 6.25

In such kind of problems, we apply the formula :
n² = a × b, where 'a' and 'b' are the extra time taken if both work individually than if both work together.
Therefore,
n² = 9 × 6.25
⇒ n = 3 × 2.5 = 7.5

Thus, working together, pipes A and B require 7.5 hours

১২১.

Two pipes that can fill a cistern in 5 hours and 8 hours respectively were used to fill two same-sized cisterns. How much time will it take to fill both the cisterns?

ক
14.87 hours
খ
6 hours
গ
6.15 hours
ঘ
10.37 hours

ব্যাখ্যা

Question: Two pipes that can fill a cistern in 5 hours and 8 hours respectively were used to fill two same-sized cisterns. How much time will it take to fill both the cisterns?

Solution:
in one hour,
1st pipe will fill = 1/5
2nd pipe will fill = 1/8

total fill up
= 1/5 + 1/8
= 13/40

so, the total time to fill two cisterns = 80/13 hours
= 6.15 hours

১২২.

A pipe fills a tank in p minutes and another pipe fills the tank in q minutes. A different pipe makes the tank empty in r minutes. If all these three pipes are opened then in how many minutes the tank will be full?

ক
ক) (p + p - q) / pqr
খ
খ) (pq + pr - pq) / pqr
গ
গ) (pq + qr - pr) / pqr
ঘ
ঘ) pqr/(qr + pr - pq)
ঙ
ঙ) None

ব্যাখ্যা

1 / (1/p + 1/q - 1/r)
= 1 / (qr+pr-pq / pqr)
= pqr / (qr + pr - pq)

১২৩.

A tank is 1/3 parts full with water. If 16 liters of water is added, the tank becomes 5/6 parts full. What is the capacity of the tank?

ক
32
খ
24
গ
48
ঘ
22

ব্যাখ্যা

Question: A tank is 1/3 parts full with water. If 16 liters of water is added, the tank becomes 5/6 parts full. What is the capacity of the tank?
(Janata RC 2022 অনুযায়ী)

Solution:
ধরি,
ট্যাংকের ধারণক্ষমতা = x লিটার

প্রশ্নমতে,
(x/3) + 16 = 5x/6
⇒ (5x/6) - (x/3) = 16
⇒ (5x - 2x)/6 = 16
⇒ 3x = 96
⇒ x = 96/3
⇒ x = 32

অর্থাৎ ট্যাংকের ধারণক্ষমতা = 32 লিটার

১২৪.

One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:

ক
3.5 hours.
খ
3 hours.
গ
4 hours.
ঘ
3.25 hours.

ব্যাখ্যা

Question: One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:

Solution:
Let the faster pipe can fill it in X minutes
in one minute it can fill up = 1/X of the tank

so the slower pipe can do it in 4X minutes
in one minute it can fill up = 1/4X of the tank

so in one minute both can fill = (1/X + 1/4X)
= 5/4X
the full tank will be filled in = 4X/5 minutes

ATQ,
4X/5 = 36
X = 45

so the slower pipe can do it in = 4 × 45 = 180 minutes = 3 hours.

১২৫.

An inline pipe takes half the time to fill a tank than an outline pipe. When both the pipes are opened, they take 9 hours to fill a tank. The outline pipe can empty the tank in -

ক
ক) 4.5 hours
খ
খ) 9 hours
গ
গ) 18 hours
ঘ
ঘ) 15 hours

ব্যাখ্যা

Question: An inline pipe takes half the time to fill a tank than an outline pipe. When both the pipes are opened, they take 9 hours to fill a tank. The outline pipe can empty the tank in -

Solution:
let, the inline pipe takes X hours to fill the tank.
so, the outline pipe takes 2X hours to empty it.

in one hour,
inline pipe fills = 1/X
outline pipe pumps out = 1/2X

total fill up = 1/X - 1/2X
= 1/2X

ATQ,
2X = 9
X = 4.5 hours

so, the outline pipe can empty the tank in = 2 × 4.5 = 9 hours

১২৬.

A bucket is 2/7 full. If 18 liters of water are added, it becomes exactly full. What is the capacity of the bucket?

ক
32 liters
খ
25.2 liters
গ
18.5 liters
ঘ
27 liters

ব্যাখ্যা

Question: A bucket is 2/7 full. If 18 liters of water are added, it becomes exactly full. What is the capacity of the bucket?

Solution:
Let the capacity of the bucket 'x' liters.
Initially the bucket has (2/7) of x = 2x/7 liters of water
After adding 18 liters then the bucket becomes full.

So we can form the equation,
(2x/7) + 18 = x
⇒ x - (2x/7) = 18
⇒ (7x - 2x)/7 = 18
⇒ 5x/7 = 18
⇒ x = (18 × 7)/5
⇒ x = 126/5
∴ x = 25.2 liters

So the capacity of the bucket is 25.2 liters.

১২৭.

Pipes A, B can fill a tank in 15 minutes and 20 minutes respectively. But pipe C can empty the full tank in 12 minutes. If all these pipes are opened simultaneously, how much time will be taken to fill the tank?

ক
ক) 30 minutes
খ
খ) 35 minutes
গ
গ) 38 minutes
ঘ
ঘ) 29 minutes

ব্যাখ্যা

Question: Pipes A, B can fill a tank in 15 minutes and 20 minutes respectively. But pipe C can empty the full tank in 12 minutes. If all these pipes are opened simultaneously, how much time will be taken to fill the tank?

Solution:
A, 1 মিনিটে পূর্ণ করে (1/15) অংশ
B, 1 মিনিটে পূর্ণ করে (1/20) অংশ
অপরদিকে,
C, 1 মিনিটে খালি করে (1/12) অংশ

সবগুলো পাইপ খুলে দিলে ট্যাংকটি পূর্ণ হবে-
= (1/15) + (1/20) − (1/12)
= (4 + 3 − 5)/60
= 2/60
= 1/30

1/30 অংশ পূর্ণ করে 1 মিনিটে
∴ 1 অংশ পূর্ণ করে 30/1 মিনিটে
= 30 মিনিটে

১২৮.

Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. This cistern will be filled in half an hour if both the pipes are opened together initially and pipe B is then turned off after X minutes. What is X?

ক
8 minutes
খ
12 minutes
গ
9 minutes
ঘ
11 minutes

ব্যাখ্যা

Question: Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. This cistern will be filled in half an hour if both the pipes are opened together initially and pipe B is then turned off after X minutes. What is X?

Solution:
Let the volume of tank = V liters
Rate of pipe A = (V/37.5) L/min
Rate of pipe B = (V/45) L/min
In X minutes (both pipes open): Part filled = (V/37.5) + (V/45) × X
= V(45 + 37.5)/(37.5 × 45) × X
= V × 82.5/(1687.5) × X
= V × (X/20.45)

In remaining time (30 - X) minutes (only pipe A): Part filled = (V/37.5) × (30 - X)
Total part filled = 1 (complete tank)
X/20.45 + (30-X)/37.5 = 1
⇒ 37.5X + 20.45(30-X) = 37.5 × 20.45
⇒ 37.5X + 613.5 - 20.45X = 766.875
⇒ 17.05X = 153.375
∴ X = 9

১২৯.

Pipes A and B can fill a tank in 8 and 10 hours respectively. Pipe C can empty it in 20 hours. If all the three pipes are opened together, then the tank will be filled in -

ক
ক) 20/3 hours
খ
খ) 20/7 hours
গ
গ) 40/3 hours
ঘ
ঘ) 40/7 hours

ব্যাখ্যা

Question: Pipes A and B can fill a tank in 8 and 10 hours respectively. Pipe C can empty it in 20 hours. If all the three pipes are opened together, then the tank will be filled in -

Solution:
in one hour, A can fill = 1/8
B can fill = 1/10
C can reduce = 1/20

so, in one-hour, total fill up = 1/8 + 1/10 - 1/20
= 7/40

Hence, it will take 40/7 hours to fill the tank if all three pipes are opened together.

১৩০.

After fillings the car's fuel tank, a driver drove from A to B and then to C. He used 2/3 portion of the fuel driving from A to B. If he used another 7 liters to drive from B to C and still had 1/4 of the tank left, how many liters does the tank hold?

ক
84 liters
খ
72 liters
গ
66 liters
ঘ
88 liters

ব্যাখ্যা

Question: After fillings the car's fuel tank, a driver drove from A to B and then to C. He used 2/3 portion of the fuel driving from A to B. If he used another 7 liters to drive from B to C and still had 1/4 of the tank left, how many liters does the tank hold?

Solution:
Let full capacity x liters
Fuel used from B to C = x - {(2x/3) + (1x/4)}
= (12x - 8x - 3x)/12
= x/12

Now,
x/12 of capacity = 7 liters
∴ x of capacity = 7 × 12 = 84 liters

১৩১.

A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

ক
ক) 3 hr 45 min
খ
খ) 3 hr 30 min
গ
গ) 4 hr 45 min
ঘ
ঘ) 3 hr 30 min

ব্যাখ্যা

Question: A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

Solution:
Time is taken by one tap to fill half the tank = 3 hr
Remaining part = 1 - 1/2 = 1/2

Part filled by four taps in one hr = 4 × (1/6) = 2/3

2/3 part filled by four taps in 1 hr
1 part filled by four taps in 3/2 hr
1/2 part filled by four taps in (3/2) × (1/2) hr
= 3/4 hr
= 45 min

So, total time taken = 3 + 45 min = 3 hr 45 min

১৩২.

An outlet pipe can empty a cistern in 5 hours. In what time will it empty 3/5 part of the cistern?

ক
4 hours
খ
3 hours
গ
5 hours
ঘ
2 hours

ব্যাখ্যা

Question: An outlet pipe can empty a cistern in 5 hours. In what time will it empty 3/5 part of the cistern?

Solution:
The outlet pipe empties one complete cistern in 5 hours
Time taken to empty 3/5 Part of the cistern = (3/5) × 5 = 3 hours.

১৩৩.

A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

ক
20 hrs.
খ
25 hrs
গ
30 hrs
ঘ
35 hrs.

ব্যাখ্যা

Suppose pipe A alone takes x hours to fill the tank in 144 min.
Then,
pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
∴ 1/x + 2/x + 4/x = 1/5
⇒ 7/x = 1/5
⇒ x = 35.

১৩৪.

A cistern can be filled by two pipes in 20 and 30 min respectively. Both pipes being open, when must the first pipe be turned off so that so that the cistern may be filled in 10 min more?

ক
ক) after 6 min.
খ
খ) after 7 min.
গ
গ) after 8 min.
ঘ
ঘ) after 8 min.

ব্যাখ্যা

In 1 min both pipes can fill = 1/20 + 1/30 = 1/12
In 10 min second pipe can fill = (1/30)×10 = 1/3 part
Part of cistern filled by both the pipes = 1 - 1/3 = 2/3
1/12 part is filled in 1 min
∴ 2/3 part will be filled in 12×2/3 = 8 min
Hence, first first pipe should be turned off after 8 min.

১৩৫.

Two pipes, X and Y can fill a tank in 30 minutes and 45 minutes, respectively. Both pipes are opened together. After how many minutes should pipe Y be turned off so that the tank is filled in 20 minutes?

ক
12 minutes
খ
15 minutes
গ
10 minutes
ঘ
8 minutes

ব্যাখ্যা

Question: Two pipes X and Y can fill a tank in 30 minutes and 45 minutes, respectively. Both pipes are opened together. After how many minutes should pipe Y be turned off so that the tank is filled in 20 minutes?

Solution:
Pipe X can fill 1 / 30 part of tank in one minute.
Pipe Y can fill 1 / 45 part of tank in one minute.
Both pipes can fill (1/30 + 1/45) part of tank in one minute.
= (3+2) / 90 = 5/90 = 1/ 18

Let, after time t minutes, we turned off the pipe Y.
according to question, [দুটি পাইপ t সময় পর্যন্ত একসাথে চলতে থাকে, বাকি সময় X পাইপটি চলে এবং সম্পূর্ণ বা 1 অংশ ট্যাংক পূর্ণ করে ]
∴ t/18 + (20-t) / 30 = 1
⇒ (5t + 60- 3t) / 90 = 1
⇒ 5t + 60 - 3t = 90
⇒ 2t = 30
⇒ t = 15

১৩৬.

Two pipes A and B can fill a tank in 40 and 60 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

ক
24 minutes
খ
20 minutes
গ
18 minutes
ঘ
15 minutes

ব্যাখ্যা

Question: Two pipes A and B can fill a tank in 40 and 60 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

Solution:
Part filled by A in 1 minute = 1/40

Part filled by B in 1 minute = 1/60

Part filled by (A + B) in 1 minute = 1/40 + 1/60 = 5/120 = 1/24

∴ Both pipes can fill the tank in 24 minutes

১৩৭.

Two pipes A and B can fill a tank in 20 hours and 30 hours respectively. If both the pipes are opened simultaneously, find after how much time should pipe B be closed so that the tank is full in 18 hours?

ক
1 hour
খ
2 hours
গ
3 hours
ঘ
4 hours
ঙ
None of these

ব্যাখ্যা

Question: Two pipes A and B can fill a tank in 20 hours and 30 hours respectively. If both the pipes are opened simultaneously, find after how much time should pipe B be closed so that the tank is full in 18 hours?

Solution:
Let the capacity of the tank be LCM (20, 30) = 60 units
Efficiency of pipe A = 60/20 = 3 units/hour
Efficiency of pipe B = 60/30 = 2 units/hour
Combined efficiency of pipes A and B = 5 units/hour

Let both A and B be opened for ‘n’ hours and then, B be closed and only A be opened for the remaining ’18 - n’ hours.
5n + 3 × (18 - n) = 60
⇒ 2n + 54 = 60
⇒ 2n = 6
∴ n = 3
Therefore, B should be closed after 3 hours.

১৩৮.

A tap can fill a tank in 48 minutes where as another tap can empty it in 2 hours. If both the taps are opened at 11 : 40 A. M, then the tank will be filled at-

ক
1 : 20 P.M
খ
12 : 40 P.M
গ
1 : 00 P.M
ঘ
1 : 30 P.M

ব্যাখ্যা

Question: A tap can fill a tank in 48 minutes where as another tap can empty it in 2 hours. If both the taps are opened at 11 : 40 A. M, then the tank will be filled at-

Solution:
1 মিনিটে পূর্ণ হয় = 1/48 অংশ

আবার,
1 মিনিটে খালি হয় = 1/(2 × 60) = 1/120 অংশ

∴ 1 মিনিটে পূর্ণ হয় = {(1/48) - (1/120)} অংশ
= (5 - 2)/240
= 3/240
= 1/80 অংশ

∴ 1/80 অংশ পূর্ণ হয় = 1 মিনিটে
1 বা সম্পূর্ণ অংশ পূর্ণ হয় = 1/(1/80) = 80 মিনিটে

সুতরাং ট্যাংকটি পূর্ণ হবে = 11 : 40 A. M + 80 মিনিটে = 1 : 00 P.M

১৩৯.

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 6 hours. The number of hours taken by C alone to fill the tank is

ক
18 hours
খ
14 hours
গ
10 hours
ঘ
9 hours

ব্যাখ্যা

Question: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 6 hours. The number of hours taken by C alone to fill the tank is

Solution:
A, B and C together can fill in one hour = 1/6
in two hours = 2/6 = 1/3

the remaining part is = 1 - 1/3 = 2/3

in 6 hours, A and B can do = 2/3
so, in one hour A and B can do = 2/(3 × 6) = 2/18

so, C can do in one hour = (A, B and C in one hour) - (A and B in one hour)
= 1/6 - 2/18
= 1/18

hence, C take 18 hours to fill the tank

১৪০.

Two pipes can fill a tank in 15 and 20 minutes respectively and a waste pipe can empty 2 gallons per minute. All the three pipes working together can fill the tank in 9 minutes. The capacity of the tank is-

ক
360 gallons
খ
260 gallons
গ
200 gallons
ঘ
350 gallons

ব্যাখ্যা

Question: Two pipes can fill a tank in 15 and 20 minutes respectively and a waste pipe can empty 2 gallons per minute. All the three pipes working together can fill the tank in 9 minutes. The capacity of the tank is-

Solution:
Let, the waste pipe empty the tank in x minutes.

According to the question,
⇒ (1/15) + (1/20) - (1/x) = (1/9)
⇒ 1/x = (1/15) + (1/20) - (1/9)
⇒ 1/x = (12 + 9 - 20)/180
⇒ 1/x = 1/180
∴ x = 180

A waste pipe can empty 2 gallons per minute In 180 minutes it can empty = 2 × 180 = 360 gallons.
∴ Capacity of the tank = 360 gallons.

১৪১.

After filling the car's fuel tank, a driver drove from P to Q and then to R. He used (2/5)th portion of the fuel driving from P to Q. If he used another 7 liters to drive from Q to R and still had (1/4)th of the tank left, how many liters does the tank hold?

ক
18 liters
খ
20 liters
গ
22 liters
ঘ
25 liters

ব্যাখ্যা

Question: After fillings the car's fuel tank, a driver drove from P to Q and then to R. He used (2/5)th portion of the fuel driving from P to Q. If he used another 7 liters to drive from Q to R and still had (1/4)th of the tank left, how many liters does the tank hold?

Solution:
Let full capacity x liters

Fuel used from Q to R = x - (2x/5 + 1x/4)
= (20x - 8x - 5x)/20
= 7x/20

Now,
7x/20 of capacity = 7 liters
x of capacity = 7 × 20/7 liters
= 20 liters

১৪২.

Three pipes A, B, and C are connected to a tank. Out of the three, A is the inlet pipe and B and C are the outlet pipes. If opened separately, A fills the tank in 10 hours, B empties the tank in 12 hours and C empties the tank in 30 hours. If all three are opened simultaneously, how much time does it take to fill/empty the tank?

ক
120 hours to fill
খ
60 hours to empty
গ
45 hours to empty
ঘ
30 hours to fill

ব্যাখ্যা

Question: Three pipes A, B, and C are connected to a tank. Out of the three, A is the inlet pipe and B and C are the outlet pipes. If opened separately, A fills the tank in 10 hours, B empties the tank in 12 hours and C empties the tank in 30 hours. If all three are opened simultaneously, how much time does it take to fill / empty the tank?

Solution:
Part of tank filled by pipe A in one hour working alone = 1/10
Part of tank emptied by pipe B in one hour working alone = 1/12
Part of tank emptied by pipe C in one hour working alone = 1/30

∴ Part of tank filled by pipes A, B and C in one hour working together = (1/10) - (1/12) - (1/30) = - (1/60)
Therefore, time taken to completely empty the tank if all pipes are opened simultaneously = 1/60 hours = 60 hours

১৪৩.

A tap can completely fill a water tank in 8 hours. The water tank has a hole in it through which the water leaks out. The leakage will cause the full water tank to empty in 10 hours. How much time will it take for the tap to fill the tank completely with the hole?

ক
18 hours
খ
20 hours
গ
24 hours
ঘ
40 hours
ঙ
48 hours

ব্যাখ্যা

Question: A tap can completely fill a water tank in 8 hours. The water tank has a hole in it through which the water leaks out. The leakage will cause the full water tank to empty in 10 hours. How much time will it take for the tap to fill the tank completely with the hole?

Solution:
Tap alone fills the tank in 8 hours
⇒ Filling rate = 1/8 tank/hour
Leakage alone empties the full tank in 10 hours
⇒ Emptying rate = 1/10 tank/hour

∴ Net rate = Filling rate - Emptying rate
= (1/8) - (1/10)
= (5 - 4)/40
= 1/40

Time to fill the tank with the hole = 1 full tank/Net rate
= 1/(1/40) hours
= 40 hours

১৪৪.

Two pipes A and B can fill a cistern in 24 and 36 minutes respectively. Both pipes are opened together, after how many minutes should B be turned off, so that the cistern be fill in 16 minutes?

ক
12 minutes.
খ
14 minutes.
গ
18 minutes.
ঘ
20 minutes.

ব্যাখ্যা

Question: Two pipes A and B can fill a cistern in 24 and 36 minutes respectively. Both pipes are opened together, after how many minutes should B be turned off, so that the cistern be fill in 16 minutes?

Solution:
A can fill the cistern in 24 minutes
So in 1 min A can fill the cistern = 1/24 part
In 16 min, A can fill the cistern = 16/24 part
= 2/3 part

Remaining part = 1 - 2/3 = 1/3 rd

As B can fill full cistern in 36 minutes
So it will fill 1/3 rd part in = (1/3 × 36) minutes.
= 12 minutes.

১৪৫.

A petrol tank is half full. If 10 gallons of petrol are removed, the tank becomes one-tenth full. What is the total capacity of the tank in gallons?

ক
25 gallons
খ
20 gallons
গ
30 gallons
ঘ
40 gallons

ব্যাখ্যা

Question: A petrol tank is half full. If 10 gallons of petrol are removed, the tank becomes one-tenth full. What is the total capacity of the tank in gallons?

Solution:
Let,
The capacity of the tank in gallons is x gallons.

According to question,
⇒ (x/2) - 10 = x/10
⇒ (x - 20)/2 = x/10
⇒ 10(x - 20) = 2x
⇒ 10x - 200 = 2x
⇒ 10x - 2x = 200
⇒ 8x = 200
∴ x = 200/8 = 25 gallons

১৪৬.

How long will it take for two pipes to fill a tank together when they can fill it alone in 14 hours and 21 hours respectively?

ক
8.4 hours
খ
8.6 hours
গ
8.8 hours
ঘ
8 hours

ব্যাখ্যা

Question: How long will it take for two pipes to fill a tank together when they can fill it alone in 14 hours and 21 hours respectively?

Solution:
together in one hour they can fill = 1/14 + 1/21 = 5/42

so, the total time to fill the tank is = 42/5 hours = 8.4 hours

১৪৭.

Pipes A and B take 36 seconds and 45 seconds, respectively, to fill the tank when used separately. Pipe C, which can empty the tank in 30 seconds, starts operating after 7 seconds of A and B being open. How much additional time will be needed to fill the tank completely?

ক
43 seconds
খ
39 seconds
গ
46 seconds
ঘ
51 seconds
ঙ
None of the above

ব্যাখ্যা

Question: Pipes A and B take 36 seconds and 45 seconds, respectively, to fill the tank when used separately. Pipe C, which can empty the tank in 30 seconds, starts operating after 7 seconds of A and B being open. How much additional time will be needed to fill the tank completely?
(পাইপ A এবং B আলাদাভাবে ৩৬ সেকেন্ড এবং ৪৫ সেকেন্ডে ট্যাংকটি পূর্ণ করতে পারে। পাইপ C, যা ৩০ সেকেন্ডে ট্যাংকটি খালি করে, A এবং B খোলা থাকা অবস্থায় ৭ সেকেন্ড পরে কাজ শুরু করে। ট্যাংকটি সম্পূর্ণ পূর্ণ করতে কত অতিরিক্ত সময় প্রয়োজন?)

Solution:
এখানে, ট্যাঙ্কের ধারণক্ষমতা (ল.সা.গু) LCM (36, 45, 30) = 180 units
∴ অতএব, পাইপ A এর দক্ষতা = 180/36 = 5 units/second
পাইপ B এর দক্ষতা = 180/45 = 4 units/second
পাইপ C এর দক্ষতা = - 180 / 30 = - 6 units/second

এখন,
প্রথম ৭ সেকেন্ডে, A এবং B খুলে রাখা হয়েছিল।
A এবং B এর যৌথ দক্ষতা = 5 + 4 = 9 units/second
অতএব, ৭ সেকেন্ডে ট্যাঙ্কের যে অংশটি পূর্ণ হয়েছে তা হচ্ছে = 7 × 9 = 63 units

ট্যাঙ্কের খালি অংশ = 180 - 63 = 117 units

এখন, সব পাইপ খুলে দেওয়া হয়েছে।
সব পাইপের যৌথ দক্ষতা = 5 + 4 - 6 = 3 units/second
অতএব, আরও সময় প্রয়োজন = 117/3 = 39 seconds.

১৪৮.

An outlet pipe can empty a cistern in 3 h. In what time will the pipe empty two-third part of the cistern?

ক
ক) 4h
খ
খ) 2h
গ
গ) 3h
ঘ
ঘ) 5h
ঙ
ঙ) 6h

ব্যাখ্যা

Time taken by pipe to empty the cistern = 3 h
Then, time taken by the pipe to empty 2/3 part = 3 × 2/3 = 2 h

১৪৯.

Two pipes A and B can separately fill a cistern in 50 minutes and 60 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened then the cistern is full in 30 minutes. In how much time the third pipe alone can empty the cistern?

ক
ক) 120 min
খ
খ) 250 min
গ
গ) 300 min
ঘ
ঘ) 325 min

ব্যাখ্যা

Question: Two pipes A and B can separately fill a cistern in 50 minutes and 60 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened then the cistern is full in 30 minutes. In how much time the third pipe alone can empty the cistern?

Solution:
Le the third pipe can empty the cistern in x min
ATQ,
(1/50) + (1/60) - 1/x = 1/30
⇒ (1/50) + (1/60) - (1/30) = 1/x
⇒ (6 + 5 -10)/300 = 1/x
⇒ 1/300 = 1/x
∴ x = 300

So, the third pipe will empty the full cistern in 300 min

১৫০.

A tank can be filled by pipe A in 2 hours and pipe B in 6 hours. At 10 A.M. pipe A was opened. At what time will the tank be filled if pipe B is opened at 11 A.M.?

ক
ক) 11 A.M.
খ
খ) 11.45 A.M.
গ
গ) 12 A.M.
ঘ
ঘ) 12.45 A.M.

ব্যাখ্যা

Question: A tank can be filled by pipe A in 2 hours and pipe B in 6 hours. At 10 A.M. pipe A was opened. At what time will the tank be filled if pipe B is opened at 11 A.M.?

Solution:
A ২ ঘণ্টায় পূর্ণ করে ১ অংশ
১ ঘণ্টায় পূর্ণ করে ১/২ অংশ

বাকি থাকে (১ - ১/২) অংশ
= ১/২ অংশ ; যা A, B একসাথে সম্পন্ন করে।

B ৬ ঘণ্টায় করে ১ অংশ কাজ
১ ঘণ্টায় করে ১/৬ অংশ কাজ

A, B ১ ঘণ্টায় করে (১/৬) + (১/২) অংশ
= ৪/৬ অংশ
= ২/৩ অংশ

A, B ২/৩ অংশ পূর্ণ করে ১ ঘণ্টায়
১/২ অংশ পূর্ণ করে ৩/(২ × ২)
= ৩/৪ ঘণ্টায়

মোট সময় = ১ + (৩/৪) = ৭/৪ ঘন্টা = ১ ঘণ্টা ৪৫ মিনিট
∴ ট্যাঙ্ক পূর্ণ হবে = ১০ টা + ১ ঘণ্টা ৪৫ মিনিট
= ১১ টা ৪৫ মিনিট

১৫১.

A pump can fill a tank with water in 2 hours. Because of a leak, it took 140 minutes to fill the tank. The leak can drain all the water of the tank in-

ক
10 hours
খ
14 hours
গ
16 hours
ঘ
20 hours

ব্যাখ্যা

Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 140 minutes to fill the tank. The leak can drain all the water of the tank in-

Solution:
একটি পাইপ চৌবাচ্চা পূর্ণ করতে পারে ২ ঘণ্টায় বা ১২০ মিনিটে
১ মিনিটে পূর্ণ করে ১/১২০ অংশ

একটি ছিদ্র থাকায় তা পূর্ণ করতে পারে ১৪০ মিনিটে
১ মিনিটে পূর্ণ হয় ১/১৪০ মিনিটে

ছিদ্র দিয়ে ১ মিনিটে খালি হয় = (১/১২০) - (১/১৪০)
= (৭ - ৬)/৮৪০
= ১/৮৪০ অংশ

সম্পূর্ণ অংশ খালি করতে সময় লাগে = ১/১/৮৪০ মিনিট
= ৮৪০ মিনিটে
= ৮৪০/৬০ ঘণ্টায়
= ১৪ ঘণ্টায়

১৫২.

Tap A can fill a tank in 6 hours, tap B can fill the same tank in 8 hours and tap C can empty the same tank in 4 hours. If all three taps A, B and C are opened together, then how much time (in hours) will be taken to fill the tank?

ক
32 hours
খ
38 hours
গ
26 hours
ঘ
28 hours
ঙ
None of the above

ব্যাখ্যা

Question: Tap A can fill a tank in 6 hours, tap B can fill the same tank in 8 hours and tap C can empty the same tank in 4 hours. If all three taps A, B and C are opened together, then how much time (in hours) will be taken to fill the tank?

Solution:
Total unit of work = 24 units [LCM of 6 hours, 8 hours and 4 hours]

Efficiency of A = 24/6 = 4
Efficiency of A = 24/8 = 3
Efficiency of A = 24/4 = 6

Total work in a hours by (A + B + C) = 4 + 3 - 6 = 1 unit

Hence, time will be taken to fill the tank = 24/1 = 24 hours

১৫৩.

A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

ক
ক) 4.5 hrs
খ
খ) 5 hrs
গ
গ) 6.5 hrs
ঘ
ঘ) 7.2 hrs

ব্যাখ্যা

Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

Solution:
চৌবাচ্চাটি 1 ঘণ্টায় পূর্ণ হয় =(1/4) - (1/9) অংশ
= (9 - 4)/36 অংশ
= 5/36
চৌবাচ্চাটির 5/36 অংশ পূর্ণ হয় = 1 ঘণ্টায়
চৌবাচ্চাটির 1 অংশ পূর্ণ হয় = (1 × 36 )/5 ঘণ্টায়
=36/5 = 7.2 ঘণ্টায়

১৫৪.

Two pipes P and Q can fill a cistern in 36 and 48 minutes respectively. Both pipes are opened together, after how many minutes should Q be turned off, so that the cistern be fill in 24 minutes?

ক
ক) 13 minutes
খ
খ) 16 minutes
গ
গ) 18 minutes
ঘ
ঘ) 21 minutes

ব্যাখ্যা

Question: Two pipes P and Q can fill a cistern in 36 and 48 minutes respectively. Both pipes are opened together, after how many minutes should Q be turned off, so that the cistern be fill in 24 minutes?

Solution:
P can fill the cistern in 36 minutes
So in 1 min P can fill the cistern = 1/36 th part
In 24 min, P can fill the cistern = 24/36 = 2/3 rd
Remaining part = 1- 2/3 = 1/3 rd
As Q can fill full cistern in 48 minutes
So it will fill 1/3 rd part in = ( 1/3 × 48) = 16 minutes.

১৫৫.

An electric pump can fill a tank in 3 hours. Because of a leak in the tank it took 7/2 hours to fill the tank. If the tank is full, how much time will the leak take to empty it?

ক
18 hours
খ
20 hours
গ
21 hours
ঘ
24 hours

ব্যাখ্যা

Question: An electric pump can fill a tank in 3 hours. Because of a leak in the tank it took 7/2 hours to fill the tank. If the tank is full, how much time will the leak take to empty it?

Solution:
pump fills 1/3 part in 1 hour

because of leak, pump fills 2/7 part in 1 hour

leak empty {(1/3) - (2/7)} part
= 1/21 part in 1 hour

∴ leak empty full tank in 21 hours

১৫৬.

Pipe B is two times efficient as pipe C. Pipe A and B together can fill an empty tank in 8 4/7 hours. Pipe A and C together can fill the same tank in 12 hours. In how many hours required filling by pipe B alone?

ক
ক) 15 hours
খ
খ) 12 hours
গ
গ) 20 hours
ঘ
ঘ) 30 hours

ব্যাখ্যা

Let, B alone filled the pipe by x hours.

Efficiency ratio of B and C =2 : 1
Time ratio of B and C = 1 : 2

Given,
(1/A + 1/B)- (1/A + 1/C) =7/60 - 1/12
⇒ 1/B - 1/C = 2/60 = 1/30
⇒ 1/x - 1/2x=1/30
⇒ 1/2x=1/30
⇒ 1/x=1/15
⇒ x = 15

B alone filled the pipe by 15 hours.

১৫৭.

One tap (A) fills a reservoir four times as fast as another tap (B). If both taps running together can fill the reservoir in 20 minutes, then how long will the slower tap (B) alone take to fill the reservoir?

ক
40 minutes
খ
1 hour
গ
1 hour 20 minutes
ঘ
1 hour 40 minutes

ব্যাখ্যা

Question: One tap (A) fills a reservoir four times as fast as another tap (B). If both taps running together can fill the reservoir in 20 minutes, then how long will the slower tap (B) alone take to fill the reservoir?

সমাধান:
ধরি,
ধীরগতির নল B একা চৌবাচ্চাটি পূর্ণ করতে সময় নেয় x মিনিট।
তাহলে, দ্রুতগতির নল A একা চৌবাচ্চাটি পূর্ণ করতে সময় নেবে x/4 মিনিট।

প্রশ্নমতে, তারা একত্রে 20 মিনিটে পূর্ণ করে। অর্থাৎ,
1/x + 1/(x/4) = 1/20
⇒ 1/x + 4/x = 1/20
⇒ (1 + 4)/x = 1/20
⇒ 5/x = 1/20
⇒ x = 5 × 20
⇒ x = 100 মিনিট
∴ x = 1 ঘণ্টা 40 মিনিট [ 60 মিনিট = 1 ঘণ্টা]

∴ ধীরগতির নলটি (B) একা চৌবাচ্চাটি পূর্ণ করতে 1 ঘন্টা 40 মিনিট সময় নেবে।

১৫৮.

A container is 2/5 full. After adding 12 liters, it becomes 4/5 full. What is the total capacity of the container?

ক
25 liters
খ
60 liters
গ
30 liters
ঘ
40 liters
ঙ
None of these

ব্যাখ্যা

Question: A container is 2/5 full. After adding 12 liters, it becomes 4/5 full. What is the total capacity of the container?

Solution:
Given that,
The container is initially 2/5 full.
After adding 12 liters, it is 4/5 full.

That means,
(4/5) - (2/5) = 2/5
So, 2/5 of the container is equal to 12 liters.

Let total capacity be x liters,
⇒ 2x/5 = 12
⇒ x = (12 × 5)/2
⇒ x = 30

So the total capacity of the container is 30 liters.

১৫৯.

Two inlet pipes can fill a tank in 10 hours and 20 hours, respectively. An outlet pipe is attached to these two pipes, and thus, the tank was filled in 12 hours. In 90 hours, the outlet pipe alone can empty how many tanks?

ক
5 tanks
খ
6 tanks
গ
8 tanks
ঘ
4 tanks

ব্যাখ্যা

Question: Two inlet pipes can fill a tank in 10 hours and 20 hours, respectively. An outlet pipe is attached to these two pipes, and thus, the tank was filled in 12 hours. In 90 hours, the outlet pipe alone can empty how many tanks?

সমাধান:
ধরি,
ছিদ্র নলটি (Outlet Pipe) একা ট্যাঙ্কটি খালি করতে P ঘন্টা সময় নেয়।

তিনটি নল একত্রে 1 ঘন্টায় পূর্ণ করে = 1/10 + 1/20 - 1/P অংশ।
প্রশ্নমতে, তিনটি নল একত্রে 12 ঘন্টায় পূর্ণ করে।
∴ 1/10 + 1/20 - 1/P = 1/12

১. ছিদ্র নলটির সময় (P) নির্ণয়:
⇒ 1/P = 1/10 + 1/20 - 1/12
হরগুলির (Denominator) ল.সা.গু. (LCM) হলো 60।
⇒ 1/P = (6 + 3 - 5)/60
⇒ 1/P = 4/60
⇒ 1/P = 1/15
⇒ P = 15 ঘন্টা।

90 ঘন্টায় যতগুলি ট্যাঙ্ক খালি করতে পারে = 90 / P
= 90/15
= 6 টি ট্যাঙ্ক।
∴ 90 ঘন্টায় ছিদ্র নলটি একা 6 টি ট্যাঙ্ক খালি করতে পারে।

১৬০.

Pipe A can fill the tank in 8 hours and pipe B can fill it in 12 hours. If pipe A is opened at 8:00 AM and pipe B is opened at 10:00 AM, then at what time will the tank be full ?

ক
11 : 48 PM
খ
1 : 36 P.M.
গ
2 : 20 P.M.
ঘ
12 : 48 PM

ব্যাখ্যা

Question: Pipe A can fill the tank in 8 hours and pipe B can fill it in 12 hours. If pipe A is opened at 8:00 AM and pipe B is opened at 10:00 AM, then at what time will the tank be full ?

Solution:
A opened 2 hours early to B
In 2 hours A can do 3 × 2 = 6 unit work
Remaining work = 24 - 6 = 18
A + B can do it in
= 18/5 hours
= 3 hours 36 minutes
∴ Tank will be full in 10 A.M. + 3 hours 36 minutes = 1 : 36 P.M.

১৬১.

Three pipes A, B, and C are connected to a tank. Out of the three, A and B are the inlet pipes and C is the outlet pipe. If opened separately, A fills the tank in 10 hours, B fills the tank in 12 hours and C empties the tank in 30 hours. If all three are opened simultaneously, how much time does it take to fill/empty the tank?

ক
13/3 hours to empty
খ
25/3 hours to fill
গ
19/3 hours to empty
ঘ
20/3 hours to fill
ঙ
17/3 hours to empty

ব্যাখ্যা

Question: Three pipes A, B, and C are connected to a tank. Out of the three, A and B are the inlet pipes and C is the outlet pipe. If opened separately, A fills the tank in 10 hours, B fills the tank in 12 hours and C empties the tank in 30 hours. If all three are opened simultaneously, how much time does it take to fill / empty the tank?

Solution:
Solution:
Part of tank filled by pipe A in one hour working alone = 1/10
Part of tank filled by pipe B in one hour working alone = 1/12
Part of tank emptied by pipe C in one hour working alone = 1/30

Part of tank filled by pipes A, B and C in one hour working together = (1/10) + (1/12) - (1/30)
= (6 + 5 - 2)/60
= 9/60
= 3/20

Therefore, time taken to completely fill the tank if A, B and C work together = 20/3 hours

১৬২.

Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is-

ক
60 gallons
খ
100 gallons
গ
120 gallons
ঘ
180 gallons

ব্যাখ্যা

Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is-

Solution:
Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24)
= 1/15 - 11/120
= - 1/40 [- ve sign means emptying]

Volume of 1/40 part = 3 gallons
∴ Volume of whole = (3 × 40) gallons
= 120 gallons.

১৬৩.

A tap can fill a tank in 8 hrs. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

ক
4 hrs
খ
5 hrs
গ
3 hrs
ঘ
2 hrs

ব্যাখ্যা

Question: A tap can fill a tank in 8 hrs. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

Solution:
Time taken by one tap to fill half the tank = 4 hrs
Remaining part after 4 hrs = (1 - 1/2) = 1/2
Part filled by the four taps in 1 hours = 4 × (1/8) = 1/2

Total time = 4 + 1 = 5 hrs

১৬৪.

A tank is filled in 6 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

ক
ক) 42 hours
খ
খ) 35 hours
গ
গ) 32 hours
ঘ
ঘ) 36 hours

ব্যাখ্যা

Question: A tank is filled in 6 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Solution:
Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.

∴1/x + 2/x + 4/x = 1/6
⇒ 7/x =1/6
⇒ x = 42 hours

১৬৫.

An outlet pipe can empty a cistern in 3 hours. In what time will empty 2/9 of the cistern?

ক
20 minutes
খ
30 minutes
গ
40 minutes
ঘ
50 minutes
ঙ
70 minutes

ব্যাখ্যা

The outlet pipe empties the one complete cistern in 3 hours
Time taken to empty 2/9 part of the cistern
= (2/9) × 3 hour
= (2/9) × 3 × 60 minutes
= (2/9) × 3 × 60 minutes
= 40 minutes

১৬৬.

Pipe A is 4 times as fast as B in filling a tank. If A takes 20 minutes to fill a tank, then what is the time taken by both the pipe A and B to fill the tank?

ক
ক) 8
খ
খ) 12
গ
গ) 16
ঘ
ঘ) 20

ব্যাখ্যা

A takes 20 minutes and it is 4 times faster than B,
it means B will take 80 minutes to fill the tank.
(1/20 + 1/80) × t = 1.
So, We get t = 16.

১৬৭.

A large tanker can be filled by two pipes A and B in 30 minutes and 20 minutes, respectively. How many minutes will it take to fill the empty tanker if only B is used in the first-half of the time and A and B are both used in the second-half of the time?

ক
21 minutes
খ
20 minutes
গ
18 minutes
ঘ
15 minutes

ব্যাখ্যা

Question: A large tanker can be filled by two pipes A and B in 30 minutes and 20 minutes, respectively. How many minutes will it take to fill the empty tanker if only B is used in the first-half of the time and A and B are both used in the second-half of the time?

Solution:
Let
the total time to fill the tank = x minutes

Part filled by (A + B) in 1 minute = 1/30 + 1/20
= (2 + 3)/60
= 1/12

(A + B) will take half of total time= (x/2) × (1/12)
The rest half will be filled by B only in half of total time = (x/2) × (1/20)

ATQ,
x/24 + x/40 = 1
⇒ (5x + 3x)/120 = 1
⇒ 8x/120 = 1
⇒ x/15 = 1
∴ x = 15

১৬৮.

Two pipes can fill a tank with water in 15 and 12 hours respectively and a third pipe can empty it in 4 hours. If the three pipes be opened, the tank will be emptied in-

ক
11 hours
খ
10 hours
গ
9 hours
ঘ
7 hours

ব্যাখ্যা

Question: Two pipes can fill a tank with water in 15 and 12 hours respectively and a third pipe can empty it in 4 hours. If the three pipes be opened, the tank will be emptied in-

Solution:
Part of the tank filled by two pipes in 1 hour = 1/15 + 1/12
= (4 + 5)/60 part
= 9/60 part
= 3/20
Part of the tank emptied by the third pipe in 1 hour = 1/4

∴ Net part of the tank emptied in 1 hour = (1/4 - 3/20) part
= (5 - 3)/20 part
= 2/20 part
= 1/10 part

1/10 Part of tank can be emptied in 1 hour
∴ The whole tank will be emptied in = 10 hours

১৬৯.

A cistern has two taps that fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the there are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty the full cistern?

ক
20 minutes
খ
15 minutes
গ
10 minutes
ঘ
8 minutes
ঙ
None

ব্যাখ্যা

Question: A cistern has two taps that fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the there are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty the full cistern?

Solution:
Let, the waste pipe can empty the cistern in x min.

According to the question,
1/12 + 1/15 - 1/x = 1/20
⇒ 1/12 + 1/15 - 1/20 = 1/x
⇒ 1/x = (5 + 4 + 3)/60
⇒ 1/x = 6/60
⇒ 1/x = 1/10
∴ x = 10

∴ The waste pipe will empty the full cistern in 10 minutes.

১৭০.

A cistern is filled by Pipe A and Pipe B together in 2 hours. Pipe A alone can fill the cistern at the rate of 100 litres per hour. Pipe B alone can fill the cistern in 4 hours. What is the capacity of the cistern?

ক
400 litres
খ
380 litres
গ
450 litres
ঘ
520 litres

ব্যাখ্যা

Question: A cistern is filled by Pipe A and Pipe B together in 2 hours. Pipe A alone can fill the cistern at the rate of 100 litres per hour. Pipe B alone can fill the cistern in 4 hours. What is the capacity of the cistern?

Solution:
Let the capacity of the cistern = x litres.

Pipe A fills at 100 litres per hour
∴ Time taken by A alone = x/100 hours
Pipe B alone fills the cistern in 4 hours
∴ Pipe B's rate = x/4 litres per hour
And Combined rate of A + B = 100 + (x/4) litres per hour

They together fill the cistern in 2 hours, so:
Combined rate = x/2 litres per hour

Therefore, 100 + (x/4) = x/2
⇒ (x/2) - (x/4) = 100
⇒ (2x - x)/4 = 100
⇒ x = 4 × 100
∴ x = 400

So the capacity of the cistern is 400 litres.

১৭১.

A pipe can fill a tank in a hours and another pipe can empty it in b (b > a) hours. If both pipes are open, in how many hours will the tank is filled?

ক
(b - a)/ab hours
খ
(a + b) hours
গ
ab/(b - a) hours
ঘ
None of these

ব্যাখ্যা

Question: A pipe can fill a tank in a hours and another pipe can empty it in b (b > a) hours. If both pipes are open, in how many hours will the tank is filled?

Solution:
Net part filled in 1 hour

∴ Net rate = Filling rate - Emptying rate
= (1/a) - (1/b)
= (b - a)/ab

∴ The tank will be filled in = ab/(b - a) hours.

১৭২.

Two pipes can fill a tank together in 8 minutes. Both pipes are opened, and after 6 minutes the first pipe is closed. It then takes 6 more minutes for the tank to be completely filled. How long would it take to fill the tank using only the second pipe?

ক
45 minutes
খ
28 minutes
গ
42 minutes
ঘ
24 minutes
ঙ
36 minutes

ব্যাখ্যা

Question: Two pipes can fill a tank together in 8 minutes. Both pipes are opened, and after 6 minutes the first pipe is closed. It then takes 6 more minutes for the tank to be completely filled. How long would it take to fill the tank using only the second pipe?

Solution:
Together, the two pipes fill the tank in 8 minutes = 1 full tank.
∴ In 1 minute, they fill = 1/8 of the tank.
∴ In 6 minutes, they fill = (1 × 6)/8 = 3/4 of the tank.

∴ Remaining part of the tank = 1 - (3/4) = 1/4.

The second pipe alone fills this 1/4 of the tank in 6 minutes.
∴ Time for the second pipe to fill the whole tank = 6 × 4 = 24 minutes.

So the second pipe alone would take 24 minutes to fill the tank.

১৭৩.

Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank if pipe A is shut?

ক
ক) 5 hr
খ
খ) `8 hr
গ
গ) 10 hr
ঘ
ঘ) 12 hr

ব্যাখ্যা

Question: Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank if pipe A is shut?

Solution:
Pipe A ২ ঘণ্টা বা ১২০ মিনিটে পূর্ণ করে ১ অংশ
১ মিনিটে পূর্ণ করে ১/১২০ অংশ

পাইপের ছিদ্র দিয়ে পানি বের হওয়ার ফলে,
১৫০ মিনিটে পূর্ণ হয় ১ অংশ
১ মিনিটে পূর্ণ হয় ১/১৫০ অংশ

১ মিনিটে খালি করে (১/১২০) - (১/১৫০) অংশ
= (৫ - ৪)/৬০০
= ১/৬০০ অংশ

সম্পূর্ণ অংশ খালি করতে সময় লাগে = ১/১/৬০০ মিনিট
= ৬০০ মিনিট
= ৬০০/৬০ ঘণ্টা
= ১০ ঘণ্টা

১৭৪.

One filling pipe P is three times faster than another filling pipe Q, if P can fill tank in 24 hours, then what is the time taken to completely fill the tank if both the pipes are opened together?

ক
ক) 12 hours
খ
খ) 16 hours
গ
গ) 18 hours
ঘ
ঘ) 14 hours

ব্যাখ্যা

Time taken by P = 24 hours
So, Q takes = 24 x 3 = 72 hours
Required time to fill the tank with both pipe = (24 x 72)/(24+72) = 18 hours

১৭৫.

A pipe can fill a cistern in 20 hours. Once the cistern is half full, three additional identical pipes are opened. How long will it take to fill the cistern completely?

ক
6 hours
খ
8 hours 30 minutes
গ
10 hours 30 minutes
ঘ
12 hours 30 minutes

ব্যাখ্যা

Question: A pipe can fill a cistern in 20 hours. Once the cistern is half full, three additional identical pipes are opened. How long will it take to fill the cistern completely?

Solution:

Work done by 1 pipe in 1 hour = 1/20
∴ Time to fill half the cistern with 1 pipe = (1/2) ÷ (1/20) = 10 hours

After cistern is half full,
three additional identical pipes are opened,
total pipes = 4
Work done by 4 pipes in 1 hour = 4 × (1/20) = 1/5
Time to fill remaining half = (1/2) ÷ (1/5)
= 2.5 hours
= 2 hours 30 minutes

∴ Total time to fill cistern = 10 + 2.5
= 12.5 hours = 12 hours 30 minutes

১৭৬.

Three pipes A, B and C can fill a tank in 10 hours. After working at it together for 3 hours, C is closed and A and B can fill the remaining part in 14 hours. How much time taken by C to fill the tank alone?

ক
ক) 18 hours
খ
খ) 20 hours
গ
গ) 22 hours
ঘ
ঘ) 24 hours

ব্যাখ্যা

Three pipes A, B, and C can fill a tank in 8 hours. A, B, and C’s 1 hour work=1/10
A, B and C's 3 hour work= 3/10 Remaining work= 1 – (3/10) = 7/10

The remaining part will be filled by A and B in 14 hours. Then,
⇒ (7/10) × (A + B) = 14
⇒ (A + B)'s whole work= 14 × (10/7)
= 20 hr (A + B)'s 1-hour work
= 1/20

A, B, and C's 1-hour work = 1/10
C's 1 hour work= (A + B + C) – (A + B)
⇒ (1/10) – (1/20)
⇒ 1/20
∴ C can fill the tank in 20 hours.

১৭৭.

One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:

ক
2 hours 24 minutes
খ
2 hours 14 minutes
গ
2 hours 36 minutes
ঘ
168 minutes
ঙ
None of the above

ব্যাখ্যা

Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:

Solution:
Let the slower pipe alone fill the tank in x minutes.

Then, the faster pipe will fill it in x/3 minutes.

∴ (1/x) + (3/x) = 1/36
⇒ 4/x = 1/36
⇒ x = 144 minutes
∴ x = 2 hours 24 minutes

১৭৮.

A tank is 30% full with water. If 18 liters of water is added the tank becomes 3/4 full. What is the capacity of the tank?

ক
25 Liters
খ
30 Liters
গ
35 Liters
ঘ
40 Liters

ব্যাখ্যা

Question: A tank is 30% full with water. If 18 liters of water is added the tank becomes 3/4 full. What is the capacity of the tank?

Solution:
Let, Capacity of the tank is x Liters.

ATQ,
30% of x + 18 = (3/4) × x
⇒ (30x/100) + 18 = 3x/4
⇒ (3x/10) + 18 = 3x/4
⇒ (3x/4) - (3x/10) = 18
⇒ (15x - 6x)/20 = 18
⇒ 9x = 18 × 20
⇒ 9x = 360
∴ x = 40

∴ The capacity of tank is 40 Liters.

১৭৯.

Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

ক
ক) 5 hour
খ
খ) 2 hours
গ
গ) 6 hours
ঘ
ঘ) 8 hours

ব্যাখ্যা

Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours
∴ 1/ x + 1/ x+6 = 1/ 4
⇒ x+6+x/ x(x+6) = 1/ 4
⇒ x² − 2x−24 = 0
⇒ (x−6)(x+4) = 0
⇒ x = 6 [neglecting the negative value of x].

১৮০.

Two pipes can fill a tank in 36 and 40 minutes respectively, and a waste pipe can empty 3.5 gallons per minutes. All three pipes working together can fill the tank in 30 minutes. The capacity of the tank is-

ক
140 gallons
খ
180 gallons
গ
240 gallons
ঘ
280 gallons
ঙ
720 gallons

ব্যাখ্যা

Question: Two pipes can fill a tank in 36 and 40 minutes respectively, and a waste pipe can empty 3.5 gallons per minutes. All three pipes working together can fill the tank in 30 minutes. The capacity of the tank is-

Solution:
Work done by the waste pipe in 1 minute = (1/30) - [(1/36) + (1/40)]
= (12 - 10 - 9)/360
= - (7/360) [Negative sign means emptying]

∴Volume of (7/360) part = 3.5 gallons
Volume of whole tank = (360 × 3.5)/7 gallons
= 180 gallons

১৮১.

Three pipes A, B and C are connected to a tank. Out of the three, A and B are the inlet pipes and C is the outlet pipe. If opened separately, A fills the tank in 10 hours and B fills the tank in 30 hours. If all three are opened simultaneously, it takes 30 minutes extra than if only A and B are opened. How much time does it take to empty the tank if only C is opened?

ক
90 hours
খ
100 hours
গ
110 hours
ঘ
120 hours
ঙ
None of these

ব্যাখ্যা

Question: Three pipes A, B and C are connected to a tank. Out of the three, A and B are the inlet pipes and C is the outlet pipe. If opened separately, A fills the tank in 10 hours and B fills the tank in 30 hours. If all three are opened simultaneously, it takes 30 minutes extra than if only A and B are opened. How much time does it take to empty the tank if only C is opened?

Solution:
Let the capacity of tank be LCM (10, 30) = 30 units
Efficiency of pipe A = 30/10 = 3 units/hour
Efficiency of pipe B = 30/30 = 1 units/hour
Combined efficiency of pipes A and B = 4 units/hour

Therefore, time taken to completely fill the tank if only A and B are opened = 30/4 = 7 hours 30 minutes
Time taken to completely fill the tank if all pipes are opened = 7 hours 30 minutes + 30 minutes = 8 hours
Combined efficiency of all pipes = 30/8 = 3.75 units/hour

Now, efficiency of pipe C = Combined efficiency of all three pipes - Combined efficiency of pipes A and B
Therefore, efficiency of pipe C = 4 - 3.75 = 0.25 units/hour
Thus, time taken to empty the tank if only C is opened = 30/0.25 = 120 hours.

১৮২.

A tank can be filled by pipe A in 5 hours and emptied by pipe B in 8 hours respectively. How much time will it take for the tank to be half full?

ক
17/3 hours
খ
20/6 hours
গ
20/3 hours
ঘ
20 hours

ব্যাখ্যা

Question: A tank can be filled by pipe A in 5 hours and emptied by pipe B in 8 hours respectively. How much time will it take for the tank to be half full?

Solution:
Pipe alone can fill the tank in = 5 hrs.
Pipe alone can empty the tank in = 8 hrs.
Let, the tank to be half full in x hrs,

ATQ,
x/5 - x/8 = 1/2
⇒ (8x - 5x)/40 = 1/2
⇒ 3x/40 = 1/2
⇒ 3x = (1/2) × 40
⇒ 3x = 20
∴ x = 20/3 hours

১৮৩.

Two pipes A and B can fill a tank in 10 and 15 minutes respectively. If both the pipes are used together, how long will it take to fill the tank?

ক
ক) 6 minutes
খ
খ) 8 minutes
গ
গ) 9 minutes
ঘ
ঘ) 10 minutes

ব্যাখ্যা

Question: Two pipes A and B can fill a tank in 10 and 15 minutes respectively. If both the pipes are used together, how long will it take to fill the tank?

Solution:
Part filled by A in 1 min = 1/10
Part filled by B in 1 min = 1/15
Part filled by ( A + B ) in 1 min = ( 1/10 + 1/15 ) = 5/30 = 1/6
∴ Both the pipes can fill the tank in 6 minutes.

১৮৪.

A tank is 7 metre long and 4 meter wide wide. At what speed should water run through a pipe 5 cm broad and 4 cm deep so that in 6 hours and 18 minutes water level in the tank rises by 4.5 meter?

ক
ক) 10 km/hr
খ
খ) 12 km/hr
গ
গ) 9 km/hr
ঘ
ঘ) 8 km/hr

ব্যাখ্যা

Rate of flow of water = x cm/minute
∴ The volume of water that flowed in the in 1 minute
= (5 × 4 × x) = 20x cu.cm.

∴ The volume of water that flowed in the tank in 6 hours 18 minutes.
i.e. (6 × 60) + 18 = 378 minutes
= 2x × 378 cu. cm.

According to question,
20x × 378 = 700 × 400 × 450
⇒ x = (700 × 400 × 450)/(20 × 378) cm/minutes
⇒ x = (700 × 400 × 450 × 60)/(20 × 378 × 100000) km/hours
⇒ x = 10 km/hrs.

১৮৫.

A pipe can fill 1/6th of a tank in 30 minutes. How much time will it take to fill two tanks?

ক
9 hours
খ
8 hours
গ
4 hours
ঘ
6 hours

ব্যাখ্যা

Question: A pipe can fill 1/6th of a tank in 30 minutes. How much time will it take to fill two tanks?

Solution:
full tank is filled in = (6 × 30) = 180 minutes = 3 hours.

two tanks is filled in = 6 hours

১৮৬.

A leak in the bottom of a tank can empty the full tank in 5 hours. An inlet pipe fills water are at the rate 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 15 hours. how many liters does the tank hold?

ক
ক) 1800
খ
খ) 1200
গ
গ) 1400
ঘ
ঘ) None of these

ব্যাখ্যা

Question: A leak in the bottom of a tank can empty the full tank in 5 hours. An inlet pipe fills water are at the rate 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 15 hours. how many liters does the tank hold?

Solution:
ছিদ্র দ্বারা ৫ ঘণ্টায় খালি হয় ১ অংশ
ছিদ্র দ্বারা ১ ঘণ্টায় খালি হয় ১/৫ অংশ

আবার, ট্যাঙ্কটি পূর্ণ থাকা অবস্থায় ইনলেট পাইপ এবং ছিদ্র দ্বারা,
১৫ ঘণ্টায় খালি হয় সম্পূর্ণ বা ১ অংশ
১ ঘণ্টায় খালি হয় ১/১৫ অংশ

[শুধু ছিদ্র দ্বারা খালি হওয়ার অংশ, ইনলেট পাইপ এবং ছিদ্র খোলা অবস্থায় খালি হওয়ার অংশের তুলনায় বেশি। তাই বড় অংশ থেকে ছোট অংশ বিয়োগ করলে শুধু ইনলেট পাইপ দ্বারা ১ ঘণ্টায় ট্যাঙ্কটি কত অংশ পূর্ণ তা পাওয়া যাবে।]

সুতরাং, ইনলেট পাইপ দ্বারা ১ ঘণ্টায় নেট পূর্ণ হয় = ১/৫ - ১/১৫ অংশ
= (৩ - ১)/১৫ অংশ
= ২/১৫ অংশ

ইনলেট পাইপ দ্বারা ২/১৫ অংশ পূর্ণ হয় ১ ঘণ্টায়
ইনলেট পাইপ দ্বারা ১ অংশ পূর্ণ হয় ১৫/২ ঘণ্টায়

এখন, ১৫/২ ঘণ্টা = (১৫/২) × ৬০ মিনিট = ৪৫০ মিনিট

আবার,
১ মিনিটে পূর্ণ হয় ৪ লিটার
৪৫০ মিনিটে পূর্ণ হয় ৪ × ৪৫০ লিটার
= ১৮০০ লিটার

∴ ট্যাঙ্কটি ধারণক্ষমতা ১৮০০ লিটার।

১৮৭.

A cistern can be filled by two pipes in 20 and 30 min respectively. Both pipes being open, when must the first pipe be turned off so that the cistern may be filled in 10 min more?

ক
5 min
খ
6 min
গ
8 min
ঘ
9 min

ব্যাখ্যা

Question: A cistern can be filled by two pipes in 20 and 30 min respectively. Both pipes being open, when must the first pipe be turned off so that the cistern may be filled in 10 min more?

Solution:
In 1 min both pipes can fill = (1/20) + (1/30)
= (3 + 2)/60
=5/60
= 1/12
In 10 min second pipe can fill = (1/30) × 10 = 1/3 part

Part of cistern filled by both the pipes = 1 - 1/3
= (3 - 1)/3
= 2/3

1/12 part is filled in 1 min
∴ 2/3 part will be filled in (12 × 2)/3 = 8 min

Hence, first pipe should be turned off after 8 min.

১৮৮.

ক
60 gallons
খ
100 gallons
গ
120 gallons
ঘ
180 gallons

ব্যাখ্যা

Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is-

Solution:
1^st pipe fill in 1 minutes = 1/20 part
2nd pipe fill in 1 minutes = 1/24 part

∴ Work done by the waste pipe in 1 minute = {1/15 - (1/20 + 1/24)} part
= (1/15 - 11/120) part
= (8 - 11)/120 part
= - (3/120) part
= - (1/40) [ −ve sign means emptying]

ATQ,
1/40 part = 3 gallons

∴ Volume of whole=(3 × 40) gallons
= 120 gallons

১৮৯.

A pipe can fill a tank in m hours and another pipe can empty it in n (n > m) hours. If both pipes are open, in how many hours will the tank is filled?

ক
mn/(m - n) hours
খ
(m + n) hours
গ
(m - n) hours
ঘ
mn/(n - m) hours

ব্যাখ্যা

Question: A pipe can fill a tank in m hours and another pipe can empty it in n (n > m) hours. If both pipes are open, in how many hours will the tank is filled?

Solution:
Net part filled in 1 hour = (1/m - 1/n)
= (n - m)/mn hours.

∴ The tank will be filled in = mn/(n - m) hours.

১৯০.

A tank is filled to three-fifths of its capacity with water. When 9 liters of water are added, the tank becomes six-sevenths full. Find the total capacity of the tank.

ক
20 liters
খ
24 liters
গ
28 liters
ঘ
35 liters

ব্যাখ্যা

Question: A tank is filled to three-fifths of its capacity with water. When 9 liters of water are added, the tank becomes six-sevenths full. Find the total capacity of the tank.

Solution:
ধরি,
ট্যাংকটির ধারণ ক্ষমতা = x লিটার

প্রশ্নমতে,
(3x/5) + 9 = 6x/7
⇒ (6x/7) - (3x/5) = 9
⇒ (30x - 21x)/35 = 9
⇒ 9x/35 = 9
⇒ 9x = 9 × 35
⇒ x = (9 × 35)/9
⇒ x = 35

∴ ট্যাংকটির ধারণ ক্ষমতা = 35 লিটার

১৯১.

Pipe 1 and pipe 2 can fill a cistern in 2 and 6 hours respectively. Pipe 3 can empty the cistern in 9 hrs. If all the pipes are opened together find the time taken to fill the cistern.

ক
ক) 1.5 hrs
খ
খ) 1.4 hrs
গ
গ) 1.8 hrs
ঘ
ঘ) 1.6 hrs

ব্যাখ্যা

Pipe 1 can fill 1/2 of the cistern in 1 hour
Pipe 2 can fill 1/6 of the cistern in 1 hour
Pipe 3 can empty 1/9 of the cistern in 1 hour
According to the question,
Time taken to full the cistern = 1/2 + 1/6 - 1/9
= 5/9
5/9 of the cistern will be filled in 1 hour.
Full cistern will be filled in = (5/9)/1
= 9/5 x 1
= 1.8 hours

১৯২.

3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

ক
10 hours
খ
12 hours
গ
14 hours
ঘ
16 hours

ব্যাখ্যা

Question: 3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

Solution:
3 pumps need 2 × 8 hours = 16 hours
1 pump needs 16 × 3 hours
∴ 4 pumps need (16 × 3)/4 hours
= 12 hours

১৯৩.

A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half ?

ক
ক) 20 min
খ
খ) 30 min
গ
গ) 40 min
ঘ
ঘ) 50 min

ব্যাখ্যা

Question: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half ?

Solution:
A ৬০ মিনিটে পূর্ণ করে ১ অংশ
১ মিনিটে পূর্ণ করে ১/৬০ অংশ

B ৪০ মিনিটে পূর্ণ করে ১ অংশ
১ মিনিটে পূর্ণ করে ১/৪০ অংশ

A,B একসাথে ১ মিনিটে পূর্ণ করে ১/৬০ + ১/৪০
= ৫/১২০
= ১/২৪ অংশ

ধরি, সময় লাগে x মিনিট

B ৪০ মিনিটে পূর্ণ করে ১ অংশ
১ মিনিটে পূর্ণ করে ১/৪০ অংশ
x/২ মিনিটে পূর্ণ করে x/৮০ অংশ

A,B একসাথে ১ মিনিটে পূর্ণ করে ১/২৪ অংশ
x/২ মিনিটে পূর্ণ করে x/৪৮ অংশ

x/৮০ + x/৪৮ = ১
⇒ ৩x + ৫x / ২৪০ = ১
⇒ ৮x = ২৪০
∴ x = ৩০ মিনিট

১৯৪.

Half of the water tank is filled manually. Tap A can fill the tank in 20 minutes and B can empty the tank in 12 minutes. If A and B are opened together, then the time taken to empty or fill the tank is -

ক
ক) 30 minutes
খ
খ) 15 minutes
গ
গ) 60 minutes
ঘ
ঘ) 45 minutes

ব্যাখ্যা

Given that,
A takes 20 minutes to fill and B takes 12 minutes to empty
Clearly,
tap B is faster than tap A.
And so, the tank will be emptied.
Half of the tank or 1/2 part of the tank is already filled.
Therefore,
we have to find the time taken to empty that 1/2 part.
Part filled by A in 1 minute = 1/20
Part emptied by B in 1 minute = 1/12.
Part emptied by (A + B) in 1 minute
= (1/12) – (1/20)
= (5 - 3)/60
= 1/30.
Therefore,
The time taken by (A + B) to empty the full tank is 30 minutes.
Time taken to empty 1/2 part of the tank is
= 30/2
= 15 minutes.

১৯৫.

A tank has a leak which would empty the completely filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minute in the tank , the leak takes 15 hours to empty the tank. How many litres of water does the tank hold?

ক
ক) 2400 litters
খ
খ) 1200 litters
গ
গ) 4500 litters
ঘ
ঘ) 7200 litters

ব্যাখ্যা

Question: A tank has a leak which would empty the completely filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minute in the tank , the leak takes 15 hours to empty the tank. How many litres of water does the tank hold?

Solution:
Let the total capacity of the tank is 30 units.
The efficiency of Leakage(Pipe A) will be 30/10 = 3
And the efficiency of the leakage (Pipe A) and another Pipe (B) which is filling the tank will be 30/15 = 2

Pipe A is emptying at 3 units/hr and when filling pipe B started then the emptying rate will come down to 2 units/hr.
∴ Filling Pipe B efficiency is 3 - 2 = 1 unit/hr
Pipe B will be fill the tank in 30/1 = 30 hrs.

The filling rate of Pipe B per minute is 4 litter
∴ Total Capacity of tank will be = (4 × 60) × 30 = 7200 litters.

১৯৬.

Three taps A, B and C fill a tank in 20 min, 15 min and 12 min, respectively. If all the taps are opened simultaneously, how long will they take to fill 40% of the tank?

ক
ক) 25 seconds
খ
খ) 40 seconds
গ
গ) 1 minutes
ঘ
ঘ) 2 minutes

ব্যাখ্যা

Part of the tank filled in 1 min by A, B and C.
1/20 + 1/15 + 1/12
= (3 + 4 + 5)/60
= 12/60
= 1/5

Therefore, Time taken by A, B and C to fill the tank = 5 min.
Therefore, Time taken by A, B and C to fill 40% of the tank
= 40% of 5 = 40/100 × 5 = 2 minutes

১৯৭.

Two pipes X and Y together can fill a tank in 72 minutes. If the size of the pipe X is thrice as Y then Y alone can fill the tank in -

ক
ক) 4 hours and 48 minutes
খ
খ) 3 hours and 48 minutes
গ
গ) 4 hours and 36 minutes
ঘ
ঘ) 3 hours and 15 minutes

ব্যাখ্যা

Let,
The time taken by Y alone to fill the tank be A minutes.
Given that, the size of the pipe X is thrice as Y.
Then, X fills the tank in A/3 minutes.
Part filled by X in 1 minute = 1/(A/3)
= 3/A
Part filled by Y in 1 minute = 1/A
Since, X and Y together take 72 minutes.
Part filled by (X + Y) in 1 minute = 1/72
i.e.,
(1/A + 3/A) = 1/72
⇒ 4/A = 1/72
A = 288 minutes
= (288/60) hours
= 4(48/60)
= 4(4/5) hours
= 4 hours and (4/5 x 60) minutes
= 4 hours and 48 minutes.
Hence, the pipe Y alone takes 4 hours and 48 minutes to fill the tank.

১৯৮.

Two pipes P and Q can fill a reservoir in 15 and 20 hours respectively. Both pipes are opened together. After how many hours should pipe P be turned off so that the reservoir is filled in 12 hours?

ক
6 hours
খ
7.5 hours
গ
8 hours
ঘ
10 hours

ব্যাখ্যা

Question: Two pipes P and Q can fill a reservoir in 15 and 20 hours respectively. Both pipes are opened together. After how many hours should pipe P be turned off so that the reservoir is filled in 12 hours?

সমাধান:
ধরি, মোট সময় 12 ঘন্টা পর চৌবাচ্চাটি পূর্ণ হয়। এই সম্পূর্ণ সময়ে কেবল নল Q খোলা ছিল।

নল Q, 20 ঘন্টায় চৌবাচ্চাটি পূর্ণ করতে পারে।
1 ঘন্টায় Q পূর্ণ করে 1/20 অংশ।
12 ঘন্টায় Q পূর্ণ করে = 12/20 অংশ
= 3/5 অংশ।

অবশিষ্ট অংশ যা P পূর্ণ করেছিল = 1 - 3/5 অংশ
= 2/5 অংশ।

নল P, 15 ঘন্টায় পূর্ণ করে 1 অংশ।
1 অংশ পূর্ণ করে 15 ঘন্টায়।
∴ 2/5 অংশ পূর্ণ করে = (15 × 2/5) ঘন্টা
= 6 ঘন্টা।

অর্থাৎ, নল P, 6 ঘন্টা কাজ করার পর বন্ধ করা হয়েছিল।
∴ নল P কে 6 ঘন্টা পর বন্ধ করতে হবে।

১৯৯.

Pipe A can fill the tank in 8 hours and pipe B can fill it in 12 hours. If pipe A is opened at 7:00 AM and pipe B is opened at 9:00 AM, then at what time will the tank be full ?

ক
ক) 12:10 PM
খ
খ) 12:30 PM
গ
গ) 11:48 PM
ঘ
ঘ) 12:36 PM

ব্যাখ্যা

A opened 2 hours early to B
In 2 hours A can do 3 × 2 = 6 unit work
Remaining work = 24 - 6 = 18
A + B can do it in
= 18/5 hours
= 3 hours 36 minutes
∴ Tank will be full in 9 A.M. + 3 hours 36 minutes = 12.36 P.M.

২০০.

A reservoir has two pipes, A and B. A can fill the reservoir 5 hours faster than B. If both together fill the reservoir in 6 hours, the reservoir will be filled by A alone in-

ক
20 hours
খ
12 hours
গ
15 hours
ঘ
10 hours

ব্যাখ্যা

Question: A reservoir has two pipes, A and B. A can fill the reservoir 5 hours faster than B. If both together fill the reservoir in 6 hours, the reservoir will be filled by A alone in-

Solution:
Let, A alone can fill the reservoir in x hours
B can fill in x + 5 hours

Both complete in 1 hour = (1/x) + (1/ x + 5)
= (2x + 5)/(x2 + 5x)

Now
1/{(2x + 5)/(x2 + 5x)} = 1/6
(x2 + 5x)/(2x + 5) = 6
⇒ x2 + 5x = 12x + 30
⇒ x2 - 7x - 30 = 0
⇒ x2 - 10x + 3x - 30 = 0
⇒ x (x - 10) + 3 (x - 10) = 0
⇒ (x - 10) (x + 3) = 0
∴ x = 10 or, x = -3 , negative value not possible

A alone can fill the reservoir in 10 hours