Time & Work, Chain Rule

PrepBank · পাতা ১১ / ১১ · ১,০০১–১,০৬৬ / ১,০৭৬

১,০০১.

A can do a piece of work in 8 days and B can do same piece of work in 12 days. A and B together complete the same piece of work and get Tk. 800 as the combined wages. A's share of the wages will be-

ক
Tk. 380
খ
Tk. 540
গ
Tk. 480
ঘ
Tk. 320

ব্যাখ্যা

Question: A can do a piece of work in 8 days and B can do same piece of work in 12 days. A and B together complete the same piece of work and get Tk. 800 as the combined wages. A's share of the wages will be-

Solution:
A এর 1 দিনের কাজ = 1/8
B এর 1 দিনের কাজ = 1/12

(A + B) একত্রে 1 দিনের কাজ = (1/8) + (1/12)
=(3 + 2)/24
= 5/24

(A + B) এর 1 দিনের কাজ অনুপাত = (1/8) : (1/12) = 3 : 2

A এর শেয়ার = {(3/5) × 800} = 480 টাকা

১,০০২.

A can do a job in 12 days and B can do the same job in 10 days. With the help of C they can do the same job in 4 days. In how many days C alone can do this job?

ক
15 days
খ
14 days
গ
13 days
ঘ
12 days

ব্যাখ্যা

Question: A can do a job in 12 days and B can do the same job in 10 days. With the help of C they can do the same job in 4 days. In how many days C alone can do this job?

Solution:
A's one day work = 1/12

B's one day work = 1/10

(A+B+C)'s one day work = 1/4

Therefore, C's one day work = (A+B+C)'s one day work - (A+B)'s one day work
So, C's one day work = 1/4 - (1/12 + 1/10) = 1/4 - {(5 + 6)/60} = 1/4 - 11/60 = (15 - 11)/60 = 4/60 = 1/15

So, C will complete the work in 15 days.

১,০০৩.

P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

ক
ক) 5(5/11)
খ
খ) 5(6/11)
গ
গ) 6(5/11)
ঘ
ঘ) 6(6/11)
ঙ
ঙ) None of these

ব্যাখ্যা

P's 1 day 1 hrs work = 1/96 part.
Q's 1 day 1 hr's work = 1/80 part.
P & Q together work in 1 hr per day = 1/96 + 1/80 = 11/480 part.
P & Q together completes in 8 hr per day = 11×8/480 = 11/60 part.
So, days required = 60/11 = 5(5/11)

১,০০৪.

If a half kg of tomato costs 80 taka, how many taka will 300 gm cost?

ক
TK. 42
খ
TK. 45
গ
TK. 48
ঘ
TK. 52

ব্যাখ্যা

Question: If a half kg of tomato costs 80 taka, how many taka will 300 gm cost?

Solution:
Let the required cost be P TK
Less weight : Less cost (Direct proportion)
500 : 300 : : 80 : P
⇒ 500/300 = 80/P
⇒5/3 = 80/P
⇒ P = (3 × 80)/5
∴ P = 48

১,০০৫.

15 machine can produce 30 phones in 30 seconds. How much time will 75 machines take to produce 150 phones?

ক
30 minutes
খ
30 seconds
গ
15 seconds
ঘ
45 seconds

ব্যাখ্যা

Question: 15 machine can produce 30 phones in 30 seconds. How much time will 75 machines take to produce 150 phones?

Solution:
15 machine 30 phones 30 sec
1 machine 1 phone = (15 × 30)/30 sec
75 machines 150 phones = (15 × 30 × 150)/(30 × 75)
= 30 sec

১,০০৬.

Twelve children take sixteen days to complete a work which can be completed by eight adults in twelve days. Sixteen adults started working and after three days ten adults left and four children joined them. How many days will they now take to complete the remaining work?

ক
ক) 3
খ
খ) 4
গ
গ) 6
ঘ
ঘ) 8

ব্যাখ্যা

1 child's 1 day's work = 1/192;
1 adults 1 day's work = 1/96.
Work done in 3 days = (1/96) × 16 × 3
= 1/2
Remaining work = {1 - (1/2)}
= 1/2.
(6 adults + 4 Children)'s 1 day's work = (6/96) + (4/192)
= 1/12
1/12 work is done by them in 1 days
1/2 work is done by them in (12 × (1/2)}
= 6 days.

১,০০৭.

A can do a piece of work in 10 days. B is 50% more efficient than A. In how many days B alone can do the same job?

ক
6.2 days
খ
6.6 days
গ
7 days
ঘ
7.2 days

ব্যাখ্যা

Question: A can do a piece of work in 10 days. B is 50% more efficient than A. In how many days B alone can do the same job?

Solution:
B is 50% more efficient than A so he will take less time to do a piece of work.

Therefore, the ratio of the time taken by A and B = 150/100 = 3 : 2

Let B takes X days to do the job.
3 : 2 = 10 : X
⇒ 3X =20
∴ X = 6.6 days

১,০০৮.

Mamun can do a piece of work in 24 days. Robin can do the same work in 30 days and Tonmoy in 40 days. Mamun and Tonmoy worked for 4 days and handed it to Rakesh. Robin worked for some days and handed it again to Mamun and Tonmoy 6 days before completing the work. For how many days did Robin work?

ক
ক) 5 days
খ
খ) 10 days
গ
গ) 8 days
ঘ
ঘ) 6 days

ব্যাখ্যা

Combined work done by Mamun and Tonmoy in 4 + 6 days (4 initial days and last 6 days)= 10/24 + 10/40
= (50 + 30)/120
= 80/120
= 2/3

∴ Remaining work = 1 - 2/3 = 1/3
Robin works for = (1/3) × 30 = 10.

১,০০৯.

A can complete a work in 24 days and B in 16 days. They work together for 6 days. How many more days will A take alone to finish the remaining work?

ক
12 days
খ
9 days
গ
10 days
ঘ
8 days

ব্যাখ্যা

Question: A can complete a work in 24 days and B in 16 days. They work together for 6 days. How many more days will A take alone to finish the remaining work?

Solution:
A একা কাজটি করতে পারে = 24 দিনে
∴ A এর একদিনের কাজ = 1/24 অংশ
এবং,
B একা কাজটি করতে পারে = 16 দিনে
∴ B এর একদিনের কাজ = 1/16 অংশ

∴ A ও B একসাথে একদিনের কাজ = (1/24) + (1/16) = (2 + 3)/48 = 5/48 অংশ
তারা 6 দিনে একসাথে কাজ করে = 6 × (5/48) = 5/8 অংশ

বাকি কাজ = 1 - (5/8) = 3/8 অংশ

অতএব,
A, 1/24 অংশ কাজ করে 1 দিনে
∴ 3/8 অংশ কাজ করে = (24 × 3)/8 = 9 দিনে

অতএব, A একা বাকি কাজ শেষ করতে ৯ দিন লাগবে।

১,০১০.

24 women or 15 men or 36 boys can finish a piece of work in 12 days, working 8 hours per day, how many men must be associated with 12 women and 6 boys to finish another piece of work 9/4 times as greater in 30 days working 6 hours a day?

ক
15 men
খ
12 men
গ
8 men
ঘ
6 men

ব্যাখ্যা

Question: 24 women or 15 men or 36 boys can finish a piece of work in 12 days, working 8 hours per day, how many men must be associated with 12 women and 6 boys to finish another piece of work 9/4 times as greater in 30 days working 6 hours a day?

Solution:
We have 15 men = 24 women
Or, 12 women = 7.5 men
Also, 36 boys = 15 men
6 boys = 15/6 = 5/2 = 2.5 men
Therefore, 12 women + 6 boys = 7.5 + 2.5 men= 10 men
Now,
The number of day's ratio is 30 : 12
The hour's ratio is 6 hours : 8 hours
The work ratio is 1 work : 9/4 work
Now,
we can say that
(30 × 6 × 1) : (12 × 8 × 9/4) = 15 : x [Where x is the total number of men]
⇒ (30 × 6 × 1) × x = (12 × 8 × 9/4) × 15
⇒ x = 18

Therefore, the total number of men = 18
So, 18 -10 = 8 men must be associated.

১,০১১.

Working 5 hours a day, A can complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in -

ক
ক) 3 days
খ
খ) 4 days
গ
গ) 6 days
ঘ
ঘ) 7 days

ব্যাখ্যা

Question: Working 5 hours a day, A can complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in -

Solution:
Working 5 hours a day, for 8 days, A can finish the work in = (5 × 8) = 40 hours
Working 6 hours a day, for 10 days, B can finish the work in = (6 × 10) = 60 hours

both together can do in one hour = 1/40 + 1/60
= (3 + 2)/120
= 5/120
= 1/24

so, it will take them 24 hours to do the work.

hence, working 8 hours a day, they need = 24/8 = 3 days

১,০১২.

A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, then the work will be completed in?

ক
4.5 days
খ
5 days
গ
9 days
ঘ
10.28 days

ব্যাখ্যা

A can complete work in 9 days.

So, percentage of work A completed in one day = 100/9 = 11.11%.

B can complete work in 12 days.

B's one day work = 100/12 = 8.33%.
A and B together can complete = 11.11 +8.33 = 19.44% of work in one day.

Now,

Take 2 days = 1 unit of time (one day of A and one of B).
In one unit of time A and B can complete work = 19.44% work.
Total time unit they need to complete whole work = 100/(19.44) = 5.14 time unit
Thus, Total time = 5.14 time unit = 5.14 × 2 = 10.28 days.

১,০১৩.

In a party, there is enough cake for 120 adults or 200 teenagers. If 150 teenagers have already eaten the cake, how many adults can be served with the remaining cake?

ক
20 adults
খ
30 adults
গ
42 adults
ঘ
50 adults

ব্যাখ্যা

Question: In a party, there is enough cake for 120 adults or 200 teenagers. If 150 teenagers have already eaten the cake, how many adults can be served with the remaining cake?

Solution:
মোট কেকের পরিমাণ = 200 জন কিশোর (Teenagers)
ইতিমধ্যে কেক খেয়েছে = 150 জন কিশোর
অবশিষ্ট কিশোরদের জন্য কেক আছে = 200 - 150 = 50 জনের

প্রশ্নমতে,
200 জন কিশোরের কেক = 120 জন প্রাপ্তবয়স্কের সমান
∴ 1 জন কিশোরের কেক = 120/200 জন প্রাপ্তবয়স্কের সমান
∴ 50 জন কিশোরের কেক = (120 × 50)/200 জন প্রাপ্তবয়স্কের সমান
= 30 জন

∴ অবশিষ্ট কেক দিয়ে আরও 30 জন প্রাপ্তবয়স্ককে পরিবেশন করা যাবে।

১,০১৪.

Aman takes twice as much as Bimol or thrice as much time as Rafi to finish a piece of work. Working together, they can finish the work in 3 days. Aman can do the work alone in -

ক
ক) 6 days
খ
খ) 12 days
গ
গ) 3 days
ঘ
ঘ) 18 days

ব্যাখ্যা

Question: Aman takes twice as much as Bimol or thrice as much time as Rafi to finish a piece of work. Working together, they can finish the work in 3 days. Aman can do the work alone in -

Solution:
Let, Aman, Bimol, and Rafi take 6x, 6x/2 = 3x, and 6x/3 = 2x respectively.

Now,
(1/6x) + (1/3x) + (1/2x) = 1/3
⇒ 6/6x = 1/3
⇒ 1/x = 1/3
⇒ x = 3

So, Aman takes = 6 × 3 = 18 days

১,০১৫.

Rakib can do a certain work in 14 days. After half the work is done Rakib got sick and skip the work for 5 days. After he returns, he started doing the rest of the work in half of his previous efficiency. Total time to finish the work is-

ক
24 days
খ
26 days
গ
30 days
ঘ
32 days

ব্যাখ্যা

Question: Rakib can do a certain work in 14 days. After half the work is done Rakib got sick and skip the work for 5 days. After he returns, he started doing the rest of the work in half of his previous efficiency. Total time to finish the work is-

Solution:
half of the work is done in 7 days and the rate of work per day is 1/14
afte the effiency became half, work per day = 1/28
∴ half of the work will take = 28/2 = 14 days

∴ total time to do the work is = 7 + 5 + 14 days
= 26 days

১,০১৬.

A shopkeeper has sufficient money to buy 50 books. On reduction in the price of each book by Tk. 4, he could buy 10 books more. How much money does he has?

ক
Tk. 1000
খ
Tk. 1200
গ
Tk. 1500
ঘ
Tk. 2000

ব্যাখ্যা

Question: A shopkeeper has sufficient money to buy 50 books. On reduction in the price of each book by Tk. 4, he could buy 10 books more. How much money does he has?

Solution:
১টি বইয়ে দাম কমে ৪ টাকা
∴ ৫০টি বইয়ে দাম কমে (৫০ × ৪) টাকা
= ২০০ টাকা

সে মোট বই কিনে (৫০ + ১০) টি
= ৬০টি

১০টি বইয়ের দাম ২০০ টাকা
∴ ৬০টি বইয়ের দাম (২০০ × ৬০)/১০ টাকা
= ১২০০ টাকা

∴ তার কাছে ১২০০ টাকা আছে।

১,০১৭.

A person crosses a 750 m long street in 5 minutes, What is his speed in km per hour?

ক
7 km/h
খ
7.5 km/h
গ
8 km/h
ঘ
9 km/h

ব্যাখ্যা

Question: A person crosses a 750 m long street in 5 minutes, What is his speed in km per hour?

Solution:
Speed = 750/(5 × 60) m/sec
= 2.5 m/sec
= 2.5 × (18/5) km/h
= 9 km/h

১,০১৮.

X can do a piece of work in 40 days. He works at it for 8 days and then Y finishes it in 16 days. How long will they together take to complete the work?

ক
ক) 13(1/3)days
খ
খ) 15 days
গ
গ) 20 days
ঘ
ঘ) 26 days
ঙ
ঙ) None of these

ব্যাখ্যা

Work done by X in 8 days = 1/40×8 = 1/5

Remaining work = 1−1/5 = 4/5

Now, 4/5 work is done by Y in 16 days
Whole work will be done by Y in = 16×5/4 = 20 days
∴ X's 1 day's work = 1/40

∴ Y's 1 day's work = 1/20

(X + Y)'s 1 day's work
=1/40 + 1/20
=3/40

Hence, X and Y will together complete the work in
= 40/3
= 13(1/3) days

১,০১৯.

If 7 meters of cloth cost Tk. 140, what is the cost of 3 meters of cloth?

ক
Tk. 45
খ
Tk. 36
গ
Tk. 60
ঘ
Tk. 90

ব্যাখ্যা

Question: If 7 meters of cloth cost Tk. 140, what is the cost of 3 meters of cloth?

Solution:
We know the cost of 7 meters of cloth Tk. 140
Cost per meter = Total cost / Number of meters = 140/7 meters = Tk. 20 per meter.

Cost of 3 meters = Unit value (cost per meter) × Number of meters
= 20 × 3
= 60

১,০২০.

35 men can complete a work in 15 days. Five days after they started working,15 more men joined them. How man days will they now take to complete the remaining work?

ক
ক) 7 days
খ
খ) 9 days
গ
গ) 12 days
ঘ
ঘ) 15 days

ব্যাখ্যা

Question: 35 men can complete a work in 15 days. Five days after they started working, 15 more men joined them. How man days will they now take to complete the remaining work?

Solution:
After working 5 days, days left = 15 - 5 = 10 dyas
and now total man = 35 + 15 = 50

35 man needed 10 days
1 man needed (10 × 35) days
50 man needed (10 × 35)/50 days = 7 days

১,০২১.

A garrison of ‘n’ men had enough food to last for 30 days. After 10 days, 50 more men joined them. If the food now lasted for 16 days, what is the value of n?

ক
180
খ
200
গ
220
ঘ
240

ব্যাখ্যা

Question: A garrison of ‘n’ men had enough food to last for 30 days. After 10 days, 50 more men joined them. If the food now lasted for 16 days, what is the value of n?

Solution:
After 10 days, the food for n men is there for 20 days.
This food can be eaten by (n + 50) men in 16 days.

So,
20n = 16(n + 50)
⇒ 20n - 16n = 800
⇒ 4n = 800
∴n = 200

১,০২২.

If 30 men can build a wall 56 meters long in 5 days, what length of a similar wall can be built by 40 men in 3 days?

ক
36.5 m
খ
44.8 m
গ
62.3 m
ঘ
92 m
ঙ
None of these

ব্যাখ্যা

Question: If 30 men can build a wall 56 meters long in 5 days, what length of a similar wall can be built by 40 men in 3 days?

Solution:
If more men work, length of wall built is more. If worked for few days, the length of wall built is also less. Hence, this problem is related to direct proportion.
The two main parameters are man and days.
Therefore,

⇒ 30 × 5 × x = 40 × 3 × 56
⇒ x = (40 × 3 × 56)/(30 × 5)
∴ x = 44.8

১,০২৩.

A ferry can carry 30 trucks or 50 motorcycles at a time. If there are 18 trucks on the ferry, how many motorcycles can be loaded onto it?

ক
20
খ
24
গ
16
ঘ
30

ব্যাখ্যা

Question: A ferry can carry 30 trucks or 50 motorcycles at a time. If there are 18 trucks on the ferry, how many motorcycles can be loaded onto it?

Explanation:
Given,
30 trucks = 50 motorcycles
∴ 1 truck = 50/30 = 5/3 motorcycles
∴ 18 trucks = 18 × 5/3 = 30 motorcycles

Maximum motorcycles on ferry = 50

∴ Remaining motorcycles that can be loaded = 50 - 30 = 20
So, the ferry can carry 20 more motorcycles along with the 18 trucks.

১,০২৪.

25 men can complete a job in 36 days. After 12 days, 5 men left. How many days will the remaining men take to finish the job?

ক
30 days
খ
18 days
গ
28 days
ঘ
20 days

ব্যাখ্যা

Question: 25 men can complete a job in 36 days. After 12 days, 5 men left. How many days will the remaining men take to finish the job?

Solution:
25 men can complete a job in 36 days
∴ Total work = 25 × 36 = 900 man-days

∴ Work done in first 12 days = 25 × 12 = 300 man-days

And,
Remaining work = 900 - 300 = 600 man-days
Remaining days = 25 - 5 = 20 men

So,
Remaining days = 600/20 = 30 days

∴ The remaining men will take 30 days to finish the job.

১,০২৫.

A man can walk a certain distance at a uniform speed in 100 days. How long will it take him to cover twice the distance at half the normal speed?

ক
50 days
খ
400 days
গ
200 days
ঘ
12.5 days
ঙ
25 days

ব্যাখ্যা

Question: A man can walk a certain distance at a uniform speed in 100 days. How long will it take him to cover twice the distance at half the normal speed?

Solution:
Earlier time = 100 days.
Distance is doubled and speed is reduced to half.
∴ time will become 2 × 2 = 4 times.
Hence now it will take 100 × 4 = 400 days

১,০২৬.

A ferry can carry 30 buses or 48 cars at a time. If there are 20 buses on the ferry, how many cars can be loaded onto it?

ক
24 cars
খ
22 cars
গ
20 cars
ঘ
18 cars
ঙ
16 cars

ব্যাখ্যা

Question: A ferry can carry 30 buses or 48 cars at a time. If there are 20 buses on the ferry, how many cars can be loaded onto it?

Solution:
Here,
30 buses = 48 cars
∴ 1 bus = 48/30 cars
∴ 20 buses = (48 × 20)/30 cars
= 32 cars

∴ Required number of cars = 48 - 32 = 16 cars

১,০২৭.

A 100 meters long train is running at a speed of 90 km per hour. It will cross a railway platform 200 m long in-

ক
8.5 sec
খ
10.5 sec
গ
10 sec
ঘ
12 sec

ব্যাখ্যা

Question: A 100 meters long train is running at a speed of 90 km per hour. It will cross a railway platform 200 m long in-

Solution:
Here,
Speed of the running train = 90 km/hr
= {90 × (5/18)} m/sec
= 25 m/sec

And length of the train is = 100 metres
Length of platform = 200 m

So, the time will taken by the train = (Length of train + Length of platform)/Speed
= (100 + 200)/25
= 300/25
= 12 sec

১,০২৮.

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done is 23 days?

ক
11 days
খ
13 days
গ
(343/17) days
ঘ
None of these

ব্যাখ্যা

Question: A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done is 23 days?

Solution:
Ratio of times taken by A and B = 100 : 130 = 10 : 13

Suppose B takes x days to do the work.
Then,
10 : 13 :: 23 : x
⇒ x = (23 × 13)/10
⇒ x = 299/10
A's 1 day's work = 1/23
B's 1 day's work = 10/299
(A + B)'s 1day's work = 1/23 + 10/299
= 23/299
= 1/13

∴ A and B together can complete the work in 13 days.

১,০২৯.

A Company employs 15 persons, each working 44 hours a week. If 4 persons are absent, how many hours a week would the rest of the persons have to work to make up the time lost?

ক
45
খ
48
গ
56
ঘ
60

ব্যাখ্যা

Question: A Company employs 15 persons, each working 44 hours a week. If 4 persons are absent, how many hours a week would the rest of the persons have to work to make up the time lost?

Solution:

একটি কোম্পানি ১৫ জন কর্মচারী নিয়োগ দেয়। প্রত্যেকে ৪৪ ঘণ্টা কাজ করে।

মোট কাজ হয় = (১৫ × ৪৪)

= ৬৬০ ঘণ্টা

৪ জন অনুপস্থিত থাকলে, বাকি থাকে = ১৫ - ৪ জন

= ১১ জন

∴ প্রত্যেকের কাজ করতে হবে = ৬৬০/১১ ঘণ্টা

= ৬০ ঘণ্টা

১,০৩০.

30 workers can manufacture 30 machines working 5 hours a day. How many workers need to be appointed extra to triple the production if they work 10 hours a day?

ক
30 workers
খ
25 workers
গ
15 workers
ঘ
40 workers
ঙ
20 workers

ব্যাখ্যা

Question: 30 workers can manufacture 30 machines working 5 hours a day. How many workers need to be appointed extra to triple the production if they work 10 hours a day?

Solution:
5 hours to manufacture 30 machines by 30 workers
∴ 1 hour to manufacture 1 machine by = (30 × 5)/30 workers
∴ 10 hours to manufacture 90 machines by = (5 × 90)/10 workers
= 45 workers

∴ Extra workers required
= (45 - 30)
= 15 workers

১,০৩১.

A can do a piece of work in 30 days. He works at it for 6 days and then B finishes it in 18 days. In what time can A and B together it?

ক
ক) 14 (1/2) days
খ
খ) 11 days
গ
গ) 13 (1/4) days
ঘ
ঘ) 12 (6/7) days
ঙ
ঙ) None of these

ব্যাখ্যা

Let 'B' alone can do the work in 'x' days
6/30 + 18/x = 1
=> x = 22.5
1/30 + 1/22.5 = 7/90
=> 90/7 = 12 (6/7) days

১,০৩২.

A contractor employs 30 men to complete a project in 40 days. After 16 days, only 40% of the work is completed. How many additional men should the contractor employ to finish the project on time?

ক
10
খ
20
গ
30
ঘ
None

ব্যাখ্যা

Question: A contractor employs 30 men to complete a project in 40 days. After 16 days, only 40% of the work is completed. How many additional men should the contractor employ to finish the project on time?

Solution:
ধরি,
সম্পূর্ণ কাজ ১০০ একক
৪০% কাজ শেষ হওয়ায় কাজ বাকী থাকে ৬০ একক
দিন বাকি থাকে ৪০ - ১৬ = ২৪ দিন

১৬ দিনে ৪০ একক কাজ করে ৩০ জন
১ দিনে ৪০ একক কাজ করে ৩০ × ১৬ জন
১ দিনে ১ একক কাজ করে ৪৮০/৪০ জন
২৪ দিনে ১ একক কাজ করে ৪৮০/(৪০ × ২৪) জন
২৪ দিনে ৬০ একক কাজ করে (৪৮০ × ৬০)/(৪০ × ২৪) জন
= ৩০ জন

∴ অতিরিক্ত লোকের প্রয়োজন নেই।

১,০৩৩.

A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 10 pieces. He cut at the rate of 45 cuts a minute. How many rolls would be cut in 24 minutes?

ক
100
খ
108
গ
112
ঘ
120

ব্যাখ্যা

Question: A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 10 pieces. He cut at the rate of 45 cuts a minute. How many rolls would be cut in 24 minutes?

Solution:
Number of cuts made to cut a roll into 10 pieces = 9

Total cuts = 24 × 45
= 1080

Number of rolls = 1080/9
= 120

১,০৩৪.

A man's regular pay is Taka 30 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid taka 1680, how many hours overtime did he work?

ক
ক) 48
খ
খ) 28
গ
গ) 16
ঘ
ঘ) 8

ব্যাখ্যা

ধরি,
Overtime করেছিল x ঘণ্টা
প্রশ্নমতে,
30 × 40 + 30 × 2 × x = 1680
1200 + 60x = 1680
60x = 1680 - 1200
60x = 480
x = 480/60
x = 8

১,০৩৫.

Mina can do a work in 3 days while Rubel can do the same work in 2 days. Both of them finish the work together and get Tk. 150. What is the share of Mina?

ক
Tk. 50
খ
Tk. 60
গ
Tk. 70
ঘ
Tk. 40

ব্যাখ্যা

Mina's wages : Rubel's wages
= Lopa's 1 day's work : Rasel's 1 day's work
= 1/3 : 1/2
= 2 : 3
∴ Mina's share = Tk.(2/5) × 150
= Tk 60

১,০৩৬.

An instructor scored a student’s test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answers. If the student answered all of the questions and received a score of 38, how many questions did that student answer correctly?

ক
38
খ
41
গ
44
ঘ
46

ব্যাখ্যা

Question: An instructor scored a student’s test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answers. If the student answered all of the questions and received a score of 38, how many questions did that student answer correctly?

Solution:
let,
c = no. of correct answers
w = no. of wrong answers.
we know total questions = 50
∴ c + w = 50
⇒ c = 50 - w ................ (1)
the teacher removed 2 times wrong answers from correct answer and gave the score as 38
c - 2w = 38 ----------- (2)

substitute (1) in (2)
50 - w - 2w = 38
⇒ 50 - 38 = 3w
⇒ 12 = 3w
∴ w = 4
Therefore no. of wrong ans = 4 which implies no. of right = 46,

১,০৩৭.

If seven persons can build a house in 30 days, how long will it take three persons to build the same house, provided that they all work at the same rate?

ক
ক) 90 days
খ
খ) 80 days
গ
গ) 70 days
ঘ
ঘ) 85 days

ব্যাখ্যা

Seven persons can build a house = 30 days

Formula Used:
Total work = Number of people × Number of days

Calculation:
Total Work = 30 × 7 = 210 units
⇒ Number of days = 210/3 = 70 days

∴ 70 days they all work at the same rate.

The correct option is 2 i.e. 70 days

১,০৩৮.

12 pumps of one type pump 300 litres of water when each is running for 18 hours per day. But a set of 16 pumps of other types pump 400 litres of water when each is running for 24 hours per day. How efficient are the former type of pumps than latter type?

ক
ক) 7/15 times more efficient
খ
খ) 7/12 times more efficient
গ
গ) 3/4 times more efficient
ঘ
ঘ) 4/3 times more efficient

ব্যাখ্যা

We know,
M₁D₁T₁W₂ = M₂D₂T₂W₁ [Men = M; Days = D; Time/Hours = T; Work = W]

Let the former type be E times efficient.
So, 1 former type pump = E x latter type pumps
So 1F = E x L
∴ 12F x 18 hours x 400 = 16L x 24 hours x 300
∴ (12 x E x L) x 18 x 400 = 16 L x 24 x 300 ------------------> Put value of F i.e. 1F
E = 4/3 = these are many times more efficient.

১,০৩৯.

A is thrice as good as B at work. A is able to finish a job in 60 days less than B. They can finish the work in _____ days if they work together.

ক
26(1/2) days
খ
18(2/3) days
গ
22(1/2) days
ঘ
24(2/3) days
ঙ
25 days

ব্যাখ্যা

If A completes a work in 1 day, B completes the same work in 3 days.
This means, difference is 2 days, if B completes the work in 3 days
Therefore, difference is 60 days, if B completes the work in 90 days

⇒ Amount of work B can do in 1 day = 1/90
Amount of work A can do in 1 day = 3 × 1/90 = 1/30

Amount of work A and B can together do in 1 day = 1/90 + 1 /30 = 4/90 = 2/45
Therefore, A and B together can do the work in 45/2 days = 22 (1/2) days

১,০৪০.

A can complete a piece of work in 18 days, B in 20 days and C in 30 days, B and C together start the work and forced to leave after 2 days. The time taken by A alone to complete the remaining work is:

ক
ক) 10 days
খ
খ) 12 days
গ
গ) 15 days
ঘ
ঘ) 16 days

ব্যাখ্যা

Question: A can complete a piece of work in 18 days, B in 20 days and C in 30 days, B and C together start the work and forced to leave after 2 days. The time taken by A alone to complete the remaining work is:

Solution:
(B+C) 2 day's work:
2 × ( 1/20 + 1/30 )
= 2 × (3+2)/60
= 1/6 part

Remaining work
= 1−1/6
= 5/6 part

A's one day's work
= 1/18 part

Time taken to complete the work
= (5/6) / (1/18) days

Hence,
Time taken to complete the work
= 5/6×18
=15 days

১,০৪১.

P works twice as fast as Q. If Q can complete a work in 12 days independently, the number of days in which P and Q can together finish the work is -

ক
ক) 3 days
খ
খ) 4 days
গ
গ) 5 days
ঘ
ঘ) 6 days

ব্যাখ্যা

Ratio of rates of working of P and Q = 2:1
So, ratio of times taken = 1 : 2
∴ P's 1 day's work = (1/6);
Q's 1 day's work = 1/12
(P + Q)'s 1 day's work = (1/6) + (1/12)
= 3/12
= 1/4
So, P and Q together can finish the work in 4 days.

১,০৪২.

5 pumps working 6 hours a day can empty a tank in 3 days. How many hours a day must 3 pumps work to empty the tank in 2 days?

ক
15 hours
খ
20 hours
গ
18 hours
ঘ
16 hours

ব্যাখ্যা

Question: 5 pumps working 6 hours a day can empty a tank in 3 days. How many hours a day must 3 pumps work to empty the tank in 2 days?

Solution:
5 pumps এর প্রয়োজনীয় সময় 3 × 6 = 18 ঘণ্টা
1 pump এর প্রয়োজনীয় সময় = 18 × 5 = 90 ঘণ্টা
3 pumps এর প্রয়োজনীয় সময় = 90/3 = 30 ঘণ্টা

∴ 3টি পাম্পকে 2 দিনে কাজটি শেষ করতে প্রতিদিন কাজ করতে হবে,
= (30/2) = 15 ঘণ্টা।

১,০৪৩.

A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in :

ক
ক) 8 days
খ
খ) 6 days
গ
গ) 4 days
ঘ
ঘ) 12 days

ব্যাখ্যা

Suppose,
A, B and C take x, x/2 and x/3 days respectively to finish the work.
Then,
(1/x) + (2/x) + (3/x) = 1/2
⇒ 6/x = 1/2
⇒ x = 12.
So, B takes 6 days to finish the work.

১,০৪৪.

An industrial loom weaves 15 centimetres of cloth every second. Approximately, how many minutes will it take for the loom to weave 45 metres of cloth?

ক
ক) 300 minutes
খ
খ) 60 minutes
গ
গ) 15 minutes
ঘ
ঘ) 5 minutes

ব্যাখ্যা

Question: An industrial loom weaves 15 centimetres of cloth every second. Approximately, how many seconds will it take for the loom to weave 45 metres of cloth?

Solution:
in one second the loom waves = 15 centimetres = 0.15 metres

so, the time to loom 45 metres is = (45/0.15) seconds
= 300 seconds
= 300/60 minutes
= 5 minutes

১,০৪৫.

A, B and C working individually can complete a task in 30 days, 15 days and 10 days respectively. If A starts working alone and B and C helps A on every 2nd and 3rd day respectively, how long will it take the task to be completed?

ক
15 days
খ
10 days
গ
12 days
ঘ
11 days

ব্যাখ্যা

Question: A, B and C working individually can complete a task in 30 days, 15 days and 10 days respectively. If A starts working alone and B and C helps A on every 2nd and 3rd day respectively, how long will it take the task to be completed?

Solution:
A একা ১ দিনে করে = ১/৩০ অংশ
B একা ১ দিনে করে = ১/১৫ অংশ
C একা ১ দিনে করে = ১/১০ অংশ

প্রথম ১০ দিনের জন্য হিসেব করে পাই,
প্রথম ১০ দিনে A কাজ করে ১০ দিন তথা = ১০/৩০ অংশ কাজ
প্রথম ১০ দিনে B কাজ করে ৫ দিন তথা = ৫/১৫ অংশ কাজ
প্রথম ১০ দিনে C কাজ করে ৩ দিন তথা = ৩/১০ অংশ কাজ
প্রথম ১০ দিনে A,B,C কাজ করে (১০/৩০) + (৫/১৫) + (৩/১০) = (১০ + ১০ + ৯)/৩০ = ২৯/৩০ অংশ
বাকি ১ - (২৯/৩০) = ১/৩০ অংশ কাজ করতে ১ দিন সময় লাগবে।

∴ মোট দিন = ১০ + ১ = ১১ দিন

১,০৪৬.

A and B can finish a job together in x days. If A alone can complete the job in x + 3 days, and B alone can complete it in x + 12 days, what is the value of x?

ক
8
খ
4
গ
6
ঘ
9
ঙ
18

ব্যাখ্যা

Question: A and B can finish a job together in x days. If A alone can complete the job in x + 3 days, and B alone can complete it in x + 12 days, what is the value of x?

Solution:
A's 1 day's work = 1/(x + 3) part
B's 1 day's work = 1/(x + 12) part
(A + B)'s 1 day's work = 1/x

ATQ,
1/(x + 3) + 1/(x + 12) = 1/x
⇒ (x + 12 + x + 3)/[(x + 3)(x + 12)] = 1/x
⇒ (2x + 15)/(x² + 15x + 36) = 1/x
⇒ 2x² + 15x = x² + 15x + 36
⇒ x² = 36
∴ x = 6

১,০৪৭.

In a training camp, 18 men can eat 20kg of rice in 3 days. How long will 3 men take to eat 40kg of rice?

ক
ক) 12 days
খ
খ) 18 days
গ
গ) 36 days
ঘ
ঘ) None

ব্যাখ্যা

Question: In a training camp, 18 men can eat 20kg of rice in 3 days. How long will 3 men take to eat 40kg of rice?

Solution:
18 জন 20কেজি চাল খায় = 3দিনে
18 জন 1কেজি চাল খায় = 3/20দিনে
1 জন 1 কেজি চাল খায় = 3 × 18/20দিনে
3 জন 1 কেজি চাল খায় = (3 × 18)/(20 × 3) দিনে
3 জন 40 কেজি চাল খায় = (3 × 18 × 40)/(20 × 3)দিনে
= 36 দিনে

১,০৪৮.

Two hundred gallons of fuel oil are purchased at Tk. 910 per gallon and are consumed at a rate of Tk. 700 worth of fuel per hour. At this rate, how many hours are required to consume the 200 gallons of fuel oil?

ক
140
খ
220
গ
260
ঘ
322
ঙ
330

ব্যাখ্যা

Question: Two hundred gallons of fuel oil are purchased at Tk. 910 per gallon and are consumed at a rate of Tk. 700 worth of fuel per hour. At this rate, how many hours are required to consume the 200 gallons of fuel oil?

Solution:
The cost for the two hundred gallons is 910 × 200 = Tk. 182000

Thus, the number of hours to consume 200 gallons of fuel is 182000/700 = 260

১,০৪৯.

Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

ক
3 : 4
খ
4 : 3
গ
5 : 3
ঘ
Data inadequate
ঙ
None of these

ব্যাখ্যা

Question: Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

Solution:
(20 × 16) = 320 women can complete the work in 1 day.
∴ 1 woman's 1 day's work = 1/320

(16 × 15) = 240 men can complete the work in 1 day.
1 man's 1 day's work = 1/240

So, required ratio = 1/240 : 1/320
= 1/3 : 1/4
= 4 : 3

১,০৫০.

10 boys or 20 girls can do a task in 10 days both. If 5 boys and 5 girls is assigned for the task, how much time will it take to complete half of the task ?

ক
20/3 days
খ
20/7 days
গ
40/3 days
ঘ
25/6 days

ব্যাখ্যা

Question: 10 boys or 20 girls can do a task in 10 days both. If 5 boys and 5 girls is assigned for the task, how much time will it take to complete half of the task ?

Solution:
10 boys can do in one day = 1/10
5 boys can do in ne day = 1/20

20 girls can do in one day = 1/10
∴ 5 girls can do in one day = 1/40

so in one day 5 boys and 5 girls can do = 1/20 + 1/40
= 3/40

∴ time required to do the full task = 40/3 days
∴ time to do half the task = 20/3 days

১,০৫১.

Animesh takes twice as much as Bimol or thrice as much time as Rafi to finish a piece of work. Working together, they can finish the work in 3 days. Animesh can do the work alone in -

ক
12 days
খ
15 days
গ
18 days
ঘ
20 days

ব্যাখ্যা

Question: Animesh takes twice as much as Bimol or thrice as much time as Rafi to finish a piece of work. Working together, they can finish the work in 3 days. Animesh can do the work alone in -

Solution:
Let, Animesh, Bimol, and Rafi take 6x, 6x/2 = 3x, and 6x/3 = 2x respectively.

Now,
(1/6x) + (1/3x) + (1/2x) = 1/3
⇒ 6/6x = 1/3
⇒ 1/x = 1/3
⇒ x = 3

So, Animesh takes = 6 × 3 = 18 days

১,০৫২.

In a cash box, there are equal numbers of 10 paisa, 25 paisa and 50 paisa coins. If it contains Tk. 170, then what is the number of 10 paisa coin?

ক
100
খ
200
গ
220
ঘ
150

ব্যাখ্যা

Question: In a cash box, there are equal numbers of 10 paisa, 25 paisa and 50 paisa coins. If it contains Tk. 170, then what is the number of 10 paisa coin?

Solution:
let, there are x numbers of 10 paisa, 25 paisa and 50 paisa coins.

We know that,
1 tk = 100 paisa

ATQ,
10x/100 + 25x/100 + 50x/100 = 170
⇒ x {(10/100) + (25/100) + (50/100)} = 170
⇒ x (1/10 + 1/4 + 1/2) = 170
⇒ x{(2 + 5 + 10)/20} = 170
⇒ 17x/20 = 170
⇒ x = (170 × 20)/17
∴ x = 200

১,০৫৩.

If the cost of gas on burning 5 burners for 5 hours a day for 7 days is Tk. 525, then how many burners can be used for 10 days at 5 hours a day for Tk. 750?

ক
11 burners
খ
5 burners
গ
13 burners
ঘ
7 burners
ঙ
3 burners

ব্যাখ্যা

Question: If the cost of gas on burning 5 burners for 5 hours a day for 7 days is Tk. 525, then how many burners can be used for 10 days at 5 hours a day for Tk. 750?

Solution:
Given that,
5 burners 5 hours a day for 7 days is Tk. 525
Total burner-hours = (5 × 5 × 7) burner-hours
= 175 burner-hours

Cost per burner-hour =(525 ÷ 175)
= 3 Tk

∴ 750 Tk. total burner-hour = (750 ÷ 3) burner-hours
= 250 burner-hours

Let, the number of burners = x

ATQ,
x × 5 × 10 = 250
⇒ x × 50 = 250
⇒ x = 250 ÷ 50
∴ x = 5

১,০৫৪.

A does 20% less work than B. If A can complete a piece of work in 15/2 hours, then B can do it in-

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

ব্যাখ্যা

Question: A does 20% less work than B. If A can complete a piece of work in 15/2 hours, then B can do it in-

Solution:
Ratio of times taken by A and B = 100/80 = 5/4
Let
B takes x days to do the work

ATQ,
5/4 = (15/2)/x
⇒ 5/4 = (15/2)/x
⇒ 5x = (15 × 4)/2
⇒ 5x = 30
∴ x = 6 hours

১,০৫৫.

Amit works twice as fast as Sagor. If Sagor can complete a work in 12 days independently, the number of days in which Amit and Sagor can together finish the work is-

ক
4 days
খ
5 days
গ
6 days
ঘ
7 days
ঙ
None

ব্যাখ্যা

Question: Amit works twice as fast as Sagor. If Sagor can complete a work in 12 days independently, the number of days in which Amit and Sagor can together finish the work is-

Solution:
Ratio of times taken by Amit and Sagor = 2 : 1
So, the ratio of time taken = 1 : 2

Since, Sagor takes 12 days, Amit takes 6 days

∴ (Amit + Sagor)'s 1 day work = (1/6) + (1/12) part
= 3/12 part
= 1/4

∴ (Amit + Sagor) can finish the work in (4/1) = 4 days

১,০৫৬.

Recollecting the progress of an assignment, a group of 24 men said that they finished a project together in 10 days. Find the number of days required to complete the same work if 30 men had worked on the same project.

ক
ক) 3 days
খ
খ) 6 days
গ
গ) 7.5 days
ঘ
ঘ) 8 days

ব্যাখ্যা

24 men complete work in 10 days.
In 1 day work done by 24 men = 1/10
In 1 day work done by 30 men = ?
∴ ? × 24 = (1/10) × 30
∴ ? = 1/8 = Amount of work done by 30 men in one day.

Thus in this case,
30 men complete the entire work in 8 days.
[If A completes a work in ''n'' days, in 1 days he completes 1/n amount of work; Conversely, if A completes 1/n amount of work in 1 day, he completes the entire work in 'n' days.]

১,০৫৭.

A worker earns Tk. 300 on the first day and spends Tk. 150 on the second day, earns Tk. 300 on the third day and again spends Tk. 150 on the fourth day, and so on. On which day would he have had Tk. 1500?

ক
16^th day
খ
17^th day
গ
19^th day
ঘ
21^st day

ব্যাখ্যা

Question: A worker earns Tk. 300 on the first day and spends Tk. 150 on the second day, earns Tk. 300 on the third day and again spends Tk. 150 on the fourth day, and so on. On which day would he have had Tk. 1500?

Solution:
1ম দিনে আয় = 300 টাকা
2য় দিনে ব্যয় = 150 টাকা
∴ প্রতি 2 দিনে জমা হয় = 300 - 150 = 150 টাকা

শুধু 1ম দিনে আয় করায় হাতে থাকে = 300 টাকা
অতএব, 1500 - 300 = 1200 টাকা আরও জমা করতে হবে।

150 টাকা জমা হয় 2 দিনে,
∴ 1200 টাকা জমা হয় = (2 × 1200)/150 = 16 দিনে

অর্থাৎ, 16 দিনের শেষে জমা থাকবে = 1200 টাকা

17-তম দিনে আবার আয় হবে = 300 টাকা
∴ মোট সঞ্চয় হবে = 1200 + 300 = 1500 টাকা

∴ 17-তম দিনে তার কাছে মোট 1500 টাকা জমা থাকবে।

১,০৫৮.

Rizvi and Shafi take a project to work together. However, Shafi falls sick after working for 20 days and Rizvi works alone on the project for the last 6 days. They submit the project in 26 days. Had Rizvi and Shafi worked on the project for all the days together, they could have submitted it in 24 days. How many days will Shafi take to complete the project alone?

ক
ক) 13 days
খ
খ) 36 days
গ
গ) 52 days
ঘ
ঘ) 72 days

ব্যাখ্যা

Let work is done by Rizvi in 1 day = 1/R & Shafi in 1/S day
Both complete work in 24 days. So in 1 day, together they complete = 1/24 = 1/R + 1/S
For 20 days both work together, so work done by them = 20(1/R + 1/S) = 5/6
Remaining work = {1 - (5/6)= 1/6} is done by Rizvi alone in 6 days
Work done by Rizvi in 6 days = 1/6 = 6(1/R)
∴ R = 36 = days needed by Rizvi to complete the work alone

According to the question,
∴ (1/36) + 1/S = 1/24
1/S = (1/24) - (1/36)
1/S = (3 - 2)/72
1/S = 1/72
S = 72 days needed by Shafi to complete the work alone.

১,০৫৯.

P and Q can do a work in 10 days, Q and R can do it in 15 days, and P and R can do it in 12 days. If all three work together, in how many days can they complete the work?

ক
8 days
খ
9 days
গ
6 days
ঘ
10 days

ব্যাখ্যা

Question: P and Q can do a work in 10 days, Q and R can do it in 15 days, and P and R can do it in 12 days. If all three work together, in how many days can they complete the work?

Solution:
P + Q can do in 1 day = 1/10 part
Q + R can do in 1 day = 1/15 part
P + R can do in 1 day = 1/12 part

∴ 2(P + Q + R) can do in 1 day = ((1/10) + (1/15) + (1/12))
= (6 + 4 + 5)/60
= 15/60
= 1/4 part

∴ P + Q + R can do in 1 day = 1/(4 × 2) part = 1/8 part

∴ Total days needed = 1/(1/8) = 8 days

১,০৬০.

A can do a piece of work in 10 days; B in 15 days. They work for 5 days. The rest of the work was finished by C in 2 days. If they get Tk. 3000 for the whole work, the daily wages of B and C together is:

ক
Tk. 450
খ
Tk. 480
গ
Tk. 520
ঘ
None of these

ব্যাখ্যা

Question: A can do a piece of work in 10 days; B in 15 days. They work for 5 days. The rest of the work was finished by C in 2 days. If they get Tk. 3000 for the whole work, the daily wages of B and C together is:

Solution:
Part of work done by A= 1/10 × 5 ⇒ 1/2
Part of work done by B = 1/15 × 5 ⇒ 1/3
Part of work done by C = 1 - (1/2 + 1/3)
⇒ 1 - 5/6
⇒ 1/6
∴ (A’s share) : (B’s share) : (C’s share) = 1/2 : 1/3 : 1/6
⇒ 3 : 2 : 1

A’s share = 3/6 × 3000 ⇒Tk. 1500
B’s share = 2/6 × 3000 ⇒Tk. 1000
C’s share = 1/6 × 3000 ⇒Tk. 500

A’s daily wages = 1500/5 ⇒ Tk. 300
B’s daily wages = 1000/5 ⇒ Tk. 200
C’s daily wages = 500/2 ⇒ Tk. 250
Daily wages of Y and Z = (200 + 250) ⇒Tk. 450

The daily wages of B and C together is Tk. 450.

১,০৬১.

A town with a population of 4000 had food packets for 30 days. After 10 days 1000 more people are added. How long will the food packets last now?

ক
ক) 20 days
খ
খ) 16 days
গ
গ) 18 days
ঘ
ঘ) 10 days

ব্যাখ্যা

Question: A town with a population of 4000 had food packets for 30 days. After 10 days 1000 more people are added. How long will the food packets last now?

Solution:
Town with a population of 4000 had food packets for 30 days.
∴ Total food packets = 4000 × 30 = 120000

Other 1000 people joined after 10 days.

Food packet consumed in first 10 days = 4000 × 10 = 40000.
∴ Remaining food packets = 120000 – 40000 = 80000

Now 1000 people more are added
∴ Total people = 4000 + 1000 = 5000.

Now, remaining food packets will be divided among 5000 people.

∴ No. of days food will last = Remaining food packets/No. of people

⇒ No. of days food will last = 80000/5000
⇒ No. of days food will last = 16

১,০৬২.

P, Q and R together can complete a work in 16 days and R alone complete the work in 20 days. If P, Q and R started the work together and after 10 days P and Q left the work, in how many days R alone complete the remaining work?

ক
12.5 days
খ
20.5 days
গ
4 days
ঘ
7.5 days
ঙ
15 days

ব্যাখ্যা

Question: P, Q and R together can complete a work in 16 days and R alone complete the work in 20 days. If P, Q and R started the work together and after 10 days P and Q left the work, in how many days R alone complete the remaining work?

Solution:
P + Q + R = 16 days
R =20 days

work (LCM of 16 and 20) = 80
( P + Q +R) ‘s work
= 80 /16
= 5 unit

Work done by R = 80 /20 = 4 unit

(P + Q + R) ‘s 10 days work
= 5 × 10
= 50 unit

Remaining work
= (80 - 50)
= 30 unit

Remaining work done by R
= 30/4
= 7.5 days

১,০৬৩.

A computer takes 50 nanoseconds to do an addition. How many additions can it do in 1 seconds?

ক
ক) 20 million
খ
খ) 25 million
গ
গ) 30 million
ঘ
ঘ) 35 million

ব্যাখ্যা

আমরা জানি
1 ন্যানো সেকেন্ড = 10^{- 9} সেকেন্ড
50 ন্যানো সেকেন্ড = 50 × 10 ^{- 9} সেকেন্ড
= 5 × 10 × 10 ^{- 9}
= 5 × 10 ^{- 8}

কম্পিউটারটি 5 × 10^{- 8}সেকেন্ডে যোগ করে 1 টি
কম্পিউটারটি 1 সেকেন্ডে যোগ করে = 1/(5 × 10 ^{- 8})
= 10⁸/5
= (10 × 10⁷)/5
= 2 × 10⁷
= 2 কোটি বা 20 মিলিয়ন

১,০৬৪.

P, Q, and R can do a job in 12 days together. If their efficiency of working be in the ratio 3 : 8 : 5, Find in what time Q can complete the same work alone?

ক
20 days
খ
22 days
গ
24 days
ঘ
26 days

ব্যাখ্যা

Question: P, Q, and R can do a job in 12 days together. If their efficiency of working be in the ratio 3 : 8 : 5, Find in what time Q can complete the same work alone.

Solution:
Given the ratio of efficiencies of P, Q & R are 3 : 8 : 5
Let, the efficiencies of P, Q & R be 3x, 8x and 5x respectively

They can do work for 12 days.
⇒ Total work = 12 × 16x = 192x

∴ The required time taken by Q to complete the job alone = 192x/8x
= 24 days.

১,০৬৫.

A box contains 96 nuts each of 100 gm and 96 bolts each of 150 gm. If the entire box weighs 25.5 kg, then find the weight of the empty box.

ক
11.5 kg
খ
5.5 kg
গ
2.5 kg
ঘ
1.5 kg

ব্যাখ্যা

Question: A box contains 96 nuts each of 100 gm and 96 bolts each of 150 gm. If the entire box weighs 25.5 kg, then find the weight of the empty box.

Solution:
১টি নাটের ওজন ১০০ গ্রাম
∴ ৯৬টি নাটের ওজন (৯৬ × ১০০) গ্রাম
= ৯৬০০ গ্রাম
= ৯.৬ কে.জি.

১টি বল্টুর ওজন ১৫০ গ্রাম
∴ ৯৬টি বল্টুর ওজন (১৫০ × ৯৬) গ্রাম
= ১৪৪০০ গ্রাম
= ১৪.৪ কে.জি.

খালি বাক্সের ওজন = (২৫.৫ - ৯.৬ - ১৪.৪) কে.জি.
= ২৫.৫ - ২৪ কে.জি.
= ১.৫ কে.জি.

১,০৬৬.

Pipe A can fill a tank in 12 hours, pipe B in 15 hours, and pipe C in 20 hours. How long will it take to fill the tank if all three pipes are used together?

ক
7 hours
খ
6 hours
গ
4 hours
ঘ
12 hours
ঙ
None of these

ব্যাখ্যা

Question: Pipe A can fill a tank in 12 hours, pipe B in 15 hours, and pipe C in 20 hours. How long will it take to fill the tank if all three pipes are used together?

Solution:
Part filled by A in 1 hour = 1/12

Part filled by B in 1 hour = 1/15

Part filled by C in 1 hour = 1/20

∴ Part filled by (A + B + C) in 1 hour
= 1/12 + (1/15) + (1/20) = (5 + 4 + 3)/60 = 12/60 = 1/5

∴ Time to fill the tank = 1/(1/5) = 5 hours