Time & Work, Chain Rule

PrepBank · পাতা ৫ / ১১ · ৪০১–৫০০ / ১,০৭৬

৪০১.

9 men bind 1800 books in 20 days. Find how many binders will be required to bind 1200 books in 24 days?

ক
6 men
খ
5 men
গ
7 men
ঘ
8 men

ব্যাখ্যা

Question: 9 men bind 1800 books in 20 days. Find how many binders will be required to bind 1200 books in 24 days?

Solution:
To bind 1800 books in 20 days binders needed 9 men
To bind 1 books in 1 days binders needed 180/1800 men
To bind 1200 books in 24 days binders needed (180 × 1200)/(1800 × 24) men
= 5 men

৪০২.

সুমন একটি কাজ ১৫ দিনে করতে পারে এবং রাজু একই কাজ ২৫ দিনে করতে পারে। সুমন ও রাজু একত্রে ৬ দিন কাজ করার পর সুমন চলে গেল। বাকি কাজ রাজু একা কত দিনে সম্পন্ন করতে পারবে?

ক
৫ দিন
খ
৭ দিন
গ
৯ দিন
ঘ
১২ দিন
ঙ
১৫ দিন

ব্যাখ্যা

প্রশ্ন: সুমন একটি কাজ ১৫ দিনে করতে পারে এবং রাজু একই কাজ ২৫ দিনে করতে পারে। সুমন ও রাজু একত্রে ৬ দিন কাজ করার পর সুমন চলে গেল। বাকি কাজ রাজু একা কত দিনে সম্পন্ন করতে পারবে?

সমাধান:
সুমন ১ দিনে করে = ১/১৫ অংশ কাজ
রাজু ১ দিনে করে = ১/২৫ অংশ কাজ

সুমন ও রাজু একত্রে,
১ দিনে করে = (১/১৫) + (১/২৫) অংশ কাজ
= (৫ + ৩)/৭৫ অংশ কাজ
= ৮/৭৫ অংশ কাজ
∴ ৬ দিনে করে = (৬ × ৮)/৭৫ অংশ কাজ
= ৪৮/৭৫ অংশ কাজ

∴ বাকী কাজ = ১ - (৪৮/৭৫) অংশ কাজ
= ২৭/৭৫ অংশ কাজ

রাজু ১ অংশ কাজ করে = ২৫ দিনে
রাজু ২৭/৭৫ অংশ কাজ করে = (২৫ × ২৭)/৭৫ দিনে
= ৯ দিনে

∴ বাকি কাজ রাজু একা সম্পন্ন করতে পারবে = ৯ দিনে।

৪০৩.

A military camp had enough food supplies to last for a certain number of days. After 10 days, 1/5 of the men desert and it is found that the provisions will now last just as long as before. How long was that?

ক
60
খ
50
গ
40
ঘ
45

ব্যাখ্যা

Question: A military camp had enough food supplies to last for a certain number of days. After 10 days, 1/5 of the men desert and it is found that the provisions will now last just as long as before. How long was that?

Solution:
Let, initially there be 'x' men having foods for y days
After 1/5 of the men left = x - (x/5)
= 4x/5

After 10 days,
x men had foods for (y - 10) days
∴ 1 man had foods for x(y - 10) days
∴ 4x/5 men had foods for = {5x(y - 10)}/4x days
= 5(y - 10)/4 days

ATQ,
5(y - 10)/4 = y
⇒ 5y - 50 = 4y
∴ y = 50

৪০৪.

If 8 machines can produce 240 units in 6 days, how many units can 12 machines produce in 4 days?

ক
240 units
খ
360 units
গ
480 units
ঘ
720 units

ব্যাখ্যা

Question: If 8 machines can produce 240 units in 6 days, how many units can 12 machines produce in 4 days?

Solution:
In 6 days 8 machines can produce 240 units
In 4 days 12 machines can produce (240 × 4 × 12)/(6 × 8) units
= 240 units

৪০৫.

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

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

ব্যাখ্যা

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

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

Here
5 : 4 = (15/2) : x
⇒ 5/4 = (15/2)/x
⇒ 5x = (15 × 4/2)
⇒ 5x = 30
∴ x = 6 hours

৪০৬.

Tanveer's investment doubles in every 5 years. If he invested Tk. 50000 in each of the years 2010, 2015, 2020 then what will be the amount received by him in 2025?

ক
Tk. 300000
খ
Tk. 700000
গ
Tk. 800000
ঘ
Tk. 1500000

ব্যাখ্যা

Question: Tanveer's investment doubles in every 5 years. If he invested Tk. 50000 in each of the years 2010, 2015, 2020 then what will be the amount received by him in 2025?

Solution:
Given,
Investment doubles every 5 years.

Tanveer invested Tk. 50000 in each of the years 2010, 2015, 2020

Now, he invested 50000 in 2010 so the amount for 2010 is 50000

In 2015 the amount gets double the amount become 100000 and then he again invest 50000 so the total amount of the year 2015 is 150000.

In 2020 the amount gets double the amount become 300000 and then he again invest 50000 so the total amount of the year 2020 is 350000.

In the year 2025 the amount gets double the amount become 700000 finally, the amount in the year 2025 is 700000.

Hence, '700000' is the correct answer.

৪০৭.

A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs. 3000 as wages for the whole work, what are the daily wages of A, B and C respectively:

ক
ক) 200, 250, 300
খ
খ) 300, 200, 250
গ
গ) 200, 300, 400
ঘ
ঘ) 250, 200, 300
ঙ
ঙ) None of these

ব্যাখ্যা

A's 5 days work = 50%
B's 5 days work = 33.33%
C's 2 days work = 16.66% [100 - (50 + 33.33)]

Ratio of contribution of work of A, B and C = 50: 33(1/3) : 16(2/3)
= 3 : 2 : 1

A's total share = Tk. 1500
B's total share = Tk. 1000
C's total share = Tk. 500

A's one day's earning = Tk.300
B's one day's earning = Tk.200
C's one day's earning = Tk.250

৪০৮.

30 men are engaged to a work by a contractor for 6 days. They work for 4 days but due to some reasons only 50% of the work will be completed. How many more men should be engaged to work to complete the work in a given period of time.

ক
ক) 28 men
খ
খ) 30 men
গ
গ) 38 men
ঘ
ঘ) 32 men

ব্যাখ্যা

Given time = 6 days

Total men = 30
let the extra men be x So,
30 × 4 = (30 + x) 2
=> 120 = 60 + 2x
=> 2x = 60
So, x = 30 men

৪০৯.

Zinnu completed the school project in 20 days. How many days will Ali take to complete the same work if he is 25% more efficient than Zinnu?

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

ব্যাখ্যা

প্রশ্ন: Zinnu completed the school project in 20 days. How many days will Ali take to complete the same work if he is 25% more efficient than Zinnu?

সমাধান:
আলী জিন্নুর চেয়ে ২৫% দক্ষ।

অর্থাৎ,
জিন্নু ১২৫ দিন সময় নিলে আলী নিবে ১০০ দিন
∴ জিন্নু ১ দিন সময় নিলে আলী নিবে ১০০/১২৫ দিন
∴ জিন্নু ২০ দিন সময় নিলে আলী নিবে (১০০ × ২০)/১২৫ দিন
= ১৬ দিন

৪১০.

If Masud can do a job in P days, while Minhaz can do the same job in Q days separately, how long will it take to finish the job if they work together?

ক
(P + Q)/PQ days
খ
PQ/(P + Q) days
গ
(P + Q) days
ঘ
(1/P) + (1/Q) days

ব্যাখ্যা

Question: If Masud can do a job in P days, while Minhaz can do the same job in Q days separately, how long will it take to finish the job if they work together?

Solution:
মাসুদ P দিনে করতে পারে কাজটির 1 অংশ
মাসুদ 1 দিনে করতে পারে কাজটির 1/P অংশ

মিনহাজ Q দিনে করতে পারে কাজটির 1 অংশ
মিনহাজ 1 দিনে করতে পারে কাজটির 1/Q অংশ

মাসুদ ও মিনহাজ 1 দিনে করতে পারে কাজটির (1/p) + (1/Q) অংশ
= (Q + P)/PQ অংশ

মাসুদ ও মিনহাজ (Q + P)/PQ অংশ কাজ করতে পারে 1 দিনে
মাসুদ ও মিনহাজ 1 অংশ কাজ করতে পারে PQ/(P + Q )দিনে

৪১১.

If 9 engines consume 24 metric tons of coal, when each is working 8 hours per day, how much coal should be available for 8 engines, each running 13 hours per day, it is given that 3 engines of the former type consume as much as 4 engines of the latter type.

ক
36 metric tons
খ
12 metric tons
গ
52 metric tons
ঘ
26 metric tons

ব্যাখ্যা

Question: If 9 engines consume 24 metric tons of coal, when each is working 8 hours per day, how much coal should be available for 8 engines, each running 13 hours per day, it is given that 3 engines of the former type consume as much as 4 engines of later type.

Solution:
We have:
The lesser engines, less coal consumed
More working hours, more coal consumed
Both the cases are directly proportional.
If three engines of former type consume 1 unit, 1 engine will consume 1/3 unit.
If four engines of latter type consume 1 unit, 1 engine will consume ¼ units.
And, less rate of consumption, less coal consumed.
Now, Number of engines = 9: 8
Working hours = 8:13
Therefore, rate of consumption = 1/3 : 1/4

Let the coal consumed by 8 engines is x metric tones
9 × 8 × 1/3 : 8 × 13 × 1/4 = 24 : x
⇒ 9 × 8 × (1/3) × x = 8 × 13 × (1/4) × 24
⇒ 24x = 624
∴ x = 26

৪১২.

If 5 spiders can catch five flies in five minutes, how many flies can 100 spiders catch in 100 minutes?

ক
100
খ
500
গ
1000
ঘ
2000

ব্যাখ্যা

Question: If 5 spiders can catch five flies in five minutes, how many flies can 100 spiders catch in 100 minutes?

Solution:
দেওয়া আছে,
৫ টি মাকড়সা ৫ মিনিটে ৫ টি পোকা ধরতে পরে
∴ ১ টি মাকড়সা ১ মিনিটে ৫/(৫ × ৫) টি পোকা ধরতে পরে
∴ ১০০ টি মাকড়সা ১০০ মিনিটে (৫ × ১০০ × ১০০)/(৫ × ৫) টি পোকা ধরতে পরে
= ২০০০ টি পোকা ধরতে পরে

৪১৩.

At what time between 7 and 8 O'clock will the hands of a clock be in the same straight line but, not together?

ক
ক) 5 min past 7
খ
খ) 5 (2/11) min past 7
গ
গ) 5 (3/11) min past 7
ঘ
ঘ) 5 (5/11) min past 7

ব্যাখ্যা

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
∴ Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.
5 min. spaces are gained in
=(60/55)×5min.
= 5(5/11) min.
∴ Required time = 5 (5/11) min. past 7

৪১৪.

To complete a certain construction job it takes 16 days for 48 workers. How many more workers are needed to complete the job in 12 days?

ক
20
খ
15
গ
18
ঘ
16

ব্যাখ্যা

Question: To complete a certain construction job it takes 16 days for 48 workers. How many more workers are needed to complete the job in 12 days?

Solution:
The work can be completed in 16 days by 48 workers
∴ The work can be completed in 12 days by (48 × 16)/12 workers
= 64 workers

More workers needed = 64 - 48 = 16

৪১৫.

Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

ক
7 hours 30 minutes
খ
8 hours
গ
8 hours 15 minutes
ঘ
8 hours 25 minutes
ঙ
None of these

ব্যাখ্যা

Question: Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

Solution:
Number of pages typed by Ravi in 1 hour = 32/6 = 16/3
Number of pages typed by Kumar in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3

Therefore Time taken by both to type 110 pages = 110 × (3/40) hours
= 33/4 hours
= 8.25 hours
= 8 hour 15 minutes

৪১৬.

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
400 days
খ
200 days
গ
50 days
ঘ
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.

৪১৭.

A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day?

ক
1/2
খ
1/3
গ
1/4
ঘ
1/5
ঙ
None of the above

ব্যাখ্যা

Question: A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day?

Solution:
A's 1 day's work = 1/18

B can do the same work in half the time taken by A, that is 9 days.
B's 1 day's work = 1/9

Then, working together, part of the same work they can finish in a day
= (1/9) + (1/18)
= (2 + 1)/18
= 3/18
= 1/6

৪১৮.

There is a provision of food in fort for 800 soldiers for 40 days. After 10 days, 200 soldiers leave the fort. Remaining food will last for how many days?

ক
ক) 25
খ
খ) 30
গ
গ) 35
ঘ
ঘ) 40

ব্যাখ্যা

Question: There is a provision of food in fort for 800 soldiers for 40 days. After 10 days, 200 soldiers leave the fort. Remaining food will last for how many days?

Solution:
After 10 days 200 soldiers leave the fort.
So, remainig days (40-10)= 30 days
& remaing soldiers (800-200)= 600 soldiers

Now, 800 soldiers can have the food for 30 days
1 soldier can have the food for 800×30 days
600 soldiers can have the food for (800×30)/600 days = 40 days
Hence the remaining food will last for 40 days.

৪১৯.

Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

ক
22
খ
25
গ
28
ঘ
32
ঙ
56

ব্যাখ্যা

Question: Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

Solution:
Machine A produces 120/40 = 3 bolts per second
Machine B produces 100/20 = 5 bolts per second.
Running simultaneously, they produce 3 + 5 = 8 bolts per second

Thus it will take them 200/8 = 25 seconds to produce 200 bolts.

৪২০.

If 12 men can finish a task in 15 days, how many days will 10 men take to finish the same task?

ক
20
খ
18
গ
16
ঘ
12

ব্যাখ্যা

Question: If 12 men can finish a task in 15 days, how many days will 10 men take to finish the same task?

Solution:
12 men can finish a task in 15 days
∴ 1 men can finish a task in 15 × 12 days
∴ 10 men can finish a task in (15 × 12)/10 days
= 18 days

৪২১.

If Machine X can produce 1,000 bolts in 4 hours and Machine Y can produce 1,000 bolts in 5 hours, in how many hours can Machines X and Y, working together at these constant rates, produce 1,000 bolts?

ক
10/9 hours
খ
20/3 hours
গ
20/9 hours
ঘ
None of these

ব্যাখ্যা

Question: If Machine X can produce 1,000 bolts in 4 hours and Machine Y can produce 1,000 bolts in 5 hours, in how many hours can Machines X and Y, working together at these constant rates, produce 1,000 bolts?

Solution:
Machine X can produce 100 bolts in 4 hrs.
In an hour X can produce 1000/4 = 250 bolts

Machine Y can produce 1000 bolts in 5 hrs.
In an hour Y can produce 1000/5 = 200 bolts

Together they can produce 250 + 200 = 450 bolts in an hour.
They will produce 1000 bolts in 1000/450 hours.
= 20/9 hours.

৪২২.

If A can do 1/4 of a work in 3 days and B can do 1/9 of the same work in 4 days, how much will A get if both work together and paid Tk 800 in all?

ক
720 Tk
খ
680 Tk
গ
600 Tk
ঘ
580 Tk
ঙ
620 Tk

ব্যাখ্যা

Question: If A can do 1/4 of a work in 3 days and B can do 1/9 of the same work in 4 days, how much will A get if both work together and paid Tk 800 in all?

Solution:
Whole work is done by A in (3 × 4) = 12 days
∴ A's 1 day's work = 1/12 part
Whole work is done by B in (4 × 9) = 36 days
∴ B's 1 day's work = 1/36 part

A's 1 day's work : B's 1 day's work
= A's wages : B's wages
= 1/12 : 1/36
= 3 : 1

∴ A's share = (800 × 3/4) Tk
= 600 Tk

৪২৩.

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

ক
4 days
খ
6 days
গ
8 days
ঘ
18 days

ব্যাখ্যা

Question: A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work-

Solution:
B can complete a work in 12 days
So, A can complete the work in 6 days

(A + B)'s 1 days work = (1/6) + (1/12) part
= (2 + 1)/12 part
= 3/12 part
= 1/4 part

So, (A + B) can complete the work in 4 days

৪২৪.

A carrier can carry 1.5 tons of products in 1 day from Teknaf to Tetulia. How much time will it be required to transfer 3 tons in two carriers?

ক
1 day
খ
2 days
গ
3 days
ঘ
5 days

ব্যাখ্যা

Question: A carrier can carry 1.5 tons of products in 1 day from Teknaf to Tetulia. How much time will it be required to transfer 3 tons in two carriers?

Solution:
১ টি কেরিয়ার ১.৫ টন মাল বহন করতে সময় নেয় ১ দিন
২ টি কেরিয়ার ৩ টন মাল বহন করতে সময় নেয় = (১.৫ × ২)/৩ = ১ দিন

৪২৫.

X can complete a work in 12 days, and Y alone can do it in 18 days. They work together for 6 days, and Z completes the remaining work in 3 days. If the total payment for the work is Tk. 600, how much should Z get?

ক
Tk. 75
খ
Tk. 90
গ
Tk. 100
ঘ
Tk. 120

ব্যাখ্যা

Question: X can complete a work in 12 days, and Y alone can do it in 18 days. They work together for 6 days, and Z completes the remaining work in 3 days. If the total payment for the work is Tk. 600, how much should Z get?

সমাধান:
X-এর একদিনের কাজ = 1/12
Y-এর একদিনের কাজ = 1/18

X ও Y একসাথে ৬ দিন কাজ করে:
= 6 × (1/12 + 1/18)
= 6 × {(3 + 2)/36} = 6 × (5/36) = 30/36 = 5/6

∴ বাকি কাজ = 1 − 5/6 = 1/6

Z এই 1/6 কাজ ৩ দিনে করেছে, অর্থাৎ Z-এর কাজ = 1/6

X-এর কাজ = 6 × 1/12 = 1/2
Y-এর কাজ = 6 × 1/18 = 1/3
Z-এর কাজ = 1/6

তাহলে অনুপাত = 1/2 : 1/3 : 1/6
= 3 : 2 : 1

মোট টাকা = 600
Z-এর অংশ = 1/(3+2+1) = 1/6
∴ Z পাবে = 600 × (1/6) = 100 টাকা

৪২৬.

Piyal can complete a work in 10 days working 8 hours a day. Sajid can complete the same work in 8 days working 10 hours a day. If both piyal and sajid work together,working 8 hours a day,in how many days can they complete the work?

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

ব্যাখ্যা

Question: Piyal can complete a work in 10 days working 8 hours a day. Sajid can complete the same work in 8 days working 10 hours a day. If both piyal and sajid work together,working 8 hours a day,in how many days can they complete the work?

Solution:
পিয়াল প্রতিদিন ৮ ঘণ্টা করে কাজ করে, ১০ দিনে একটি কাজ করতে পারে।
মোট ঘণ্টা = ১০ × ৮ ঘণ্টা
= ৮০ ঘণ্টা

সাজিদ প্রতিদিন ১০ ঘণ্টা করে ৮ দিনে একটি কাজ করতে পারে।
মোট ঘণ্টা = ১০ × ৮ ঘণ্টা
= ৮০ ঘণ্টা

দুইজন একসাথে এক ঘণ্টায় করতে পারে = (১/৮০) + (১/৮০) অংশ
= ২/৮০ অংশ
= ১/৪০ অংশ

সম্পূর্ণ অংশ করতে সময় লাগে = ৪০ ঘণ্টা

দৈনিক ৮ ঘণাট করে কাজ করলে, সময় লাগে = ৪০/৮ দিন
= ৫ দিন

৪২৭.

Amit and Sumit can plough a field in 4 days. Sumit alone can plough the field in 6 days. In how many days will Amit alone plough the field?

ক
8 days
খ
10 days
গ
12 days
ঘ
16 days

ব্যাখ্যা

Question: Amit and Sumit can plough a field in 4 days. Sumit alone can plough the field in 6 days. In how many days will Amit alone plough the field?

Solution:
সুমিত একদিনে করে ১/৬ অংশ কাজ

আমিত একদিনে করে (১/৪) - (১/৬)
= ১/১২ অংশ কাজ

সম্পূর্ণ কাজটি করতে অমিতের সময় লাগবে = ১২ দিন

৪২৮.

Tickets for all but 100 seats in a 10000-seat stadium were sold. Of the tickets sold, 20% were sold at half price and the remaining tickets were sold at the full price of Tk. 2. What was the total revenue from ticket sales?

ক
Tk. 15840
খ
Tk. 17820
গ
Tk. 18000
ঘ
Tk. 19800
ঙ
Tk. 21780

ব্যাখ্যা

Question: Tickets for all but 100 seats in a 10000-seat stadium were sold. Of the tickets sold, 20% were sold at half price and the remaining tickets were sold at the full price of Tk. 2. What was the total revenue from ticket sales?

Solution:
100 are not sold from 10000
So seats sold = 9900

20% of 9900 is = (20/100) × 9900 = 1980
and remaining 80% is 9900 - 1980 = 7920.

each ticket cost Tk. 2 and 1980 seats cost Tk. 1

So, total revenue = 2 × 7920 + 1980 = 17820

৪২৯.

30 men can complete a road construction project in 20 days, working 8 hours a day. How many men need to be appointed extra to complete the same work in 12 days, working 10 hours a day?

ক
8
খ
9
গ
10
ঘ
15

ব্যাখ্যা

Question: 30 men can complete a road construction project in 20 days, working 8 hours a day. How many men need to be appointed extra to complete the same work in 12 days, working 10 hours a day?

Solution:
দৈনিক ৮ ঘণ্টা করে কাজ করে ২০ দিনে শেষ করতে লোক লাগে ৩০ জন
∴ দৈনিক ১ ঘণ্টা করে কাজ করে ১ দিনে শেষ করতে লোক লাগে (৩০ × ৮ × ২০) জন
∴ দৈনিক ১০ ঘণ্টা করে কাজ করে ১২ দিনে শেষ করতে লোক লাগে (৩০ × ৮ × ২০)/(১০ × ১২) জন
= ৪০ জন

∴ অতিরিক্ত লোক লাগবে = (৪০ - ৩০) = ১০ জন

৪৩০.

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) 4.5 days
ঘ
ঘ) 5.4 days

ব্যাখ্যা

Working 5 hours a day, A can complete the work in 8 days i.e.
= 5 × 8 = 40 hours
Working 6 hours a day, B can complete the work in 10 days i.e.
= 6 × 10 = 60 hours
(A + B)'s 1 hour's work,
= 1/40 + 1/60 = (3+2)/ 120
= 5/120
= 1/24
Hence, A and B can complete the work in 24 hours i.e. they require 3 days to complete the work.

৪৩১.

Rakib and Kabila are working on an assignment. Rakib takes 6 hours to type 32 pages on a computer, while Kabila takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 220 pages?

ক
14 hour 15 minutes
খ
12 hour 30 minutes
গ
8 hour 15 minutes
ঘ
16 hour 30 minutes

ব্যাখ্যা

Question: Rakib and Kabila are working on an assignment. Rakib takes 6 hours to type 32 pages on a computer, while Kabila takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 220 pages?

Solution:
Number of pages typed by Rakib in 1 hour = 32/6 = 16/3
Number of pages typed by Kabila in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3

Therefore Time taken by both to type 220 pages = 220 × (3/40) hours
= 33/4 hours
= 16.5 hours
= 16 hour 30 minutes

৪৩২.

Subhash can copy 50 pages in 10 hours; Subhash and Prakash together can copy 300 pages in 40 hours. In how much time can Prakash copy 30 pages?

ক
ক) 11 hours
খ
খ) 12 hours
গ
গ) 15 hours
ঘ
ঘ) 18 hours

ব্যাখ্যা

Number of page copied by Subhash and Prakash in 1 hour
= 300/40
= 7.5 pages;

Subhash copied pages in one hour
= 50/10
= 5 pages

Hence, Prakash copied pages in one hour
= 7.5 - 5
= 2.5

Thus, Prakash can copied 30 pages in
= 30/2.5
= 12 hours

৪৩৩.

A tank is filled using 20 buckets, each having a capacity of 10 liters. How many buckets would be required to fill the same tank if each bucket can hold 40 liters of water?

ক
8 buckets
খ
5 buckets
গ
10 buckets
ঘ
12 buckets

ব্যাখ্যা

Question: A tank is filled using 20 buckets, each having a capacity of 10 liters. How many buckets would be required to fill the same tank if each bucket can hold 40 liters of water?

Solution:

Total capacity of the tank = 20 × 10 = 200 liters

∴ Number of buckets needed with 40-liter buckets = 200 ÷ 40
= 5 buckets

৪৩৪.

In a dairy farm, 20 cows eat 20 bags in 20 days. In how many days one cow will eat one bag of husk?

ক
ক) 10 days
খ
খ) 1/10 days
গ
গ) 20 days
ঘ
ঘ) 40 days

ব্যাখ্যা

We know,
Indirect proportion: Less cows (↓) More days (↑)
Direct proportion: Less bags (↓) Less days (↓)

20 : x :: { 1 : 20 ------ (Cows); 20 : 1 -------(Bags)}
1 × 20 × x = 20 × 1 × 20
⇒ x = (20 × 1 × 20)/(1 × 20)
⇒ x = 20 Days.

৪৩৫.

If A can do 1/4 of a work in 3 days and B can do 1/6 of the same work in 4 days, how much will A get if both work together and are paid Tk. 180 in all?

ক
ক) Tk. 60
খ
খ) Tk. 120
গ
গ) Tk. 90
ঘ
ঘ) Tk. 180

ব্যাখ্যা

A in 3 days can do = 1/4 of a work
∴ In 1 day = 1/12 of a work
B in 4 days can do = 1/6 of a work
∴ In 1 day = 1/24 of a work
In terms of ratio, A : B = 1/12 : 1/24 = 2 : 1
∴ A gets = 180 × 2/(2+1) = Tk. 120

৪৩৬.

A and B together can paint a wall in 3 days. A can do it alone in 5 days. How many days would it take B to do this job alone?

ক
0.2
খ
7.5
গ
5.0
ঘ
6.4
ঙ
None of these

ব্যাখ্যা

Question: A and B together can paint a wall in 3 days. A can do it alone in 5 days. How many days would it take B to do this job alone?

Solution:
A's 1 day's work 1/5
A and B's 1 day's work 1/3

∴ B's 1 day's work = 1/3 - 1/5 = (5 - 3)/15 = 2/15

2/15 part of job done by B in 1 day
∴ Full job done by B in (15/2) days = 7.5 days

৪৩৭.

A can complete a project in 20 days and B can complete the same project in 30 days. A and B start working on the project together and A quits 10 days before the project is expected to be completed. How many days in total will the project take to complete?

ক
ক) 16 days
খ
খ) 18 days
গ
গ) 23 days
ঘ
ঘ) 27 days

ব্যাখ্যা

A ও B একত্রে 1 দিনে করে = (1/20 + 1/30) = 1/12 অংশ
B একা 10 দিনে করে = 10/30 অংশ = 1/3 অংশ
অবশিষ্ট কাজ = (1 - 1/3) = 2/3 অংশ

এখন, A ও B একত্রে 1/12 অংশ করে 1 দিনে
A ও B একত্রে 1 অংশ করে = (12 × 1) দিনে
A ও B একত্রে 2/3 অংশ করে = (12 × 2) /3 = 8 দিনে
∴ মোট সময় লাগে = (10 + 8) দিন = 18 দিন

৪৩৮.

If Rafi and Suman together can complete a job in 12 days. If Rafi alone can finish the job in 20 days, in how many days can Suman alone complete the work?

ক
25 days
খ
60 days
গ
45 days
ঘ
30 days

ব্যাখ্যা

Question: If Rafi and Suman together can complete a job in 12 days. If Rafi alone can finish the job in 20 days, in how many days can Suman alone complete the work?

Solution:
Rafi and Suman together can complete a piece of work in 12 days
Rafi and Suman together can complete in 1 day = 1/12

Rafi alone in 20 days
Rafi alone in one day = 1/20

∴ Suman complete in one day = (1/12) - (1/20)
= (5 - 3)/60
= 2/60
= 1/30

∴ Suman can complete the work in 30 days

৪৩৯.

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

ক
40
খ
35
গ
45
ঘ
50
ঙ
None of these

ব্যাখ্যা

Question: 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

Solution:
Let,
1 man's 1 day's work = x and 1 woman's 1 day's work = y.
Then,
4x + 6y = 1/8 and 3x + 7y = 1/10
Solving the two equations, we get: x = 11/400 , y = 1/400

∴ 1 woman's 1 day's work = 1/400
10 women's 1 day's work = (1/400) × 10 = 1/40
Hence, 10 women will complete the work in 40 days.

৪৪০.

A takes three times as much time as B or twice as much time as C to finish a piece of work. Working together, they can finish the work in 3 days. B can do the work alone in how many days?

ক
14 days
খ
8 days
গ
6 days
ঘ
10 days

ব্যাখ্যা

Question: A takes three times as much time as B or twice as much time as C to finish a piece of work. Working together, they can finish the work in 3 days. B can do the work alone in how many days?

Solution:
ধরা যাক,
A, B ও C যথাক্রমে কাজটি শেষ করতে সময় লাগে x, x/3, এবং x/2 দিন।

তারা একসাথে ৩ দিনে কাজ শেষ করে।
অর্থাৎ তাদের একদিনের কাজ হলো 1/3।

∴ A + B + C এর একদিনের কাজ = (1/x) + (3/x) + (2/x)
= (1 + 3 + 2)/x
= 6/x

এখন,
6/x = 1/3
∴ x = 18

∴ B একা কাজ শেষ করতে সময় নেবে = 18/3 = 6 দিন।

৪৪১.

Ali can type 60 pages in 20 minutes. Sara can type 12 pages in 12 minutes. Working together, how many pages can they type in 30 minutes?

ক
100 pages
খ
220 pages
গ
120 pages
ঘ
130 pages
ঙ
110 pages

ব্যাখ্যা

Question: Ali can type 60 pages in 20 minutes. Sara can type 12 pages in 12 minutes. Working together, how many pages can they type in 30 minutes?

Solution:
Ali can type in 1 min = 60/20 = 3 pages
Sara can type in 1 min = 12/12 = 1 page

∴ Working together they can type in 1 min = (3 + 1) pages = 4 pages

∴ They can type in 30 min = 4 × 30 pages = 120 pages

৪৪২.

If 18 pumps can raise 2170 tonnes of water in 10 days, working 7 hours a day; in how many days will 16 pumps raise 1736 tonnes of water, working 9 hours a day?

ক
ক) 6
খ
খ) 7
গ
গ) 8
ঘ
ঘ) 9

ব্যাখ্যা

Let,
The required number of days be x.
Less pumps, More days[Indirect proportion]
Less weight, Less days [Direct proportion]
More hours/days, Less days [Indirect proportion]
{Pumps(16 : 18) , Weight (2170 : 1736), Hours/Day(9 :7)} :: 10 : x
∴ (16 × 2170 × 9 × x) = (18 × 1736 × 7 × 10)
⇒ x = (18 × 1736 × 7 × 10)/(16 × 2170 × 9)
= 7.

৪৪৩.

35 men can make 70 toys in 8 days by working 8 hours a day. How many days will 56 men need to make 84 toys by working 12 hours every day?

ক
4 days
খ
5 days
গ
3 days
ঘ
6 days

ব্যাখ্যা

Question: 35 men can make 70 toys in 8 days by working 8 hours a day. How many days will 56 men need to make 84 toys by working 12 hours every day?

Solution:
Total man-hours for 70 toys:
35 × 8 × 8 = 2240 man-hours
So, Man-hours per toy = 2240/70 = 32

Total man-hours for 84 toys:
84 × 32 = 2688 man-hours
Total man-hours per day for 56 men working 12 hours:
56 × 12 = 672 man-hours/day

∴ Time to complete work = 2688/672 = 4 days

৪৪৪.

6 men can pack 12 boxes in 7 days by working for 7 hours a day. In how many days can 14 men pack 18 boxes if they work for 9 hours a day?

ক
3.5 days
খ
5 days
গ
7.5 days
ঘ
12 days

ব্যাখ্যা

If 'w₁' work is done by 'm₁' men by working for 'h₁' hours per day in 'd₁' days & 'w₂' is work done by men 'm₂' working for 'h₂' hours per day in 'd₂' days,
then,
m₁d₁h₁/w₁ = m₂d₂h₂/w₂

Since we need to find 'd₂', we can rearrange the formula as
d2 = (m₁d₁h₁w₂)/(m₂d₂h₂w₁)
= (6 x 7 x 7 x 18)/(14 x 9 x 12)
= 3.5 days

৪৪৫.

Robi and Bobi together can paint a wall in 16 days. Robi can do it alone in 20 days. How many days would it take Bobi to do this work alone?

ক
48 days
খ
40 days
গ
24 days
ঘ
80 days
ঙ
96 days

ব্যাখ্যা

Question: Robi and Bobi together can paint a wall in 16 days. Robi can do it alone in 20 days. How many days would it take Bobi to do this work alone?

Solution:
Robi's 1 day's work 1/20
Robi's and Bobi's 1 day's work 1/16
∴ Bobi's 1 day's work = (1/16) - (1/20)
= (5 - 4)/80
= 1/80

1/80 part of the job done by Bobi in 1 day
∴ Full work done by Bobi in (80/1) days
= 80 days

৪৪৬.

Rakib can do a piece of work in 15 days, Rakib and Asif together can do in 12 days. If Asif does the work only for half a day daily then in how many days the work will be completed ?

ক
3/20 days
খ
20/3 days
গ
40/3 days
ঘ
3/40 days

ব্যাখ্যা

Question: Rakib can do a piece of work in 15 days, Rakib and Asif together can do in 12 days. If Asif does the work only for half a day daily then in how many days the work will be completed ?

Solution:

Rakib's 1 day work = 1/15

Since, Rakib and Asif can together complete in 12 days
i.e. (Rakib + Asif)'s 1 day work = 1/12

Then,
Asif's 1 day work,
= (1/12) - (1/15) = (5 - 4)/60 = 1/60

If Asif Works only for half a day daily, then his 1 day work becomes (1/2) × (1/60)
= (1/120)

Therefore, 1 day work of both Rakib and Asif,
=(1/15) + (1/120) = ( 8 + 1)/120 = 9/120

Hence, the work will be completed in 120/9 = 40/3 days

৪৪৭.

How many times in a day, the hands of a clock are straight?

ক
24 times
খ
44 times
গ
62 times
ঘ
22 times

ব্যাখ্যা

Question: How many times in a day, the hands of a clock are straight?

Solution:
The no of times the hands of a clock are straight = 22 times in 12 hours

∴ In a day or 24 hours, the hands of a clock are straight for 22×2 times.
= 44 times

৪৪৮.

3 men, 4 women, and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

ক
5
খ
6
গ
7
ঘ
8

ব্যাখ্যা

Question: 3 men, 4 women, and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

Solution:
Let 1 woman's 1 day work = x.
Then, 1 man's 1 day work = x/2 and 1 child's 1 day work x/4.

ATQ,
(3x/2) + 4x + (6x/4) = 1/7
⇒ 28x/4 = 1/7
∴ x = 1/49

1 woman alone can complete the work in 49 days.
So, to complete the work in 7 days, number of women required = 49/7 = 7.

৪৪৯.

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

ক
5 hours
খ
6 hours
গ
7 hours
ঘ
8 hours

ব্যাখ্যা

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

Solution:
40 ঘন্টার জন্য রাব্বির নিয়মিত বেতন = (30 × 40) = 1200 টাকা।
Overtime এর টাকার পরিমান = (1680 - 1200) টাকা = 480 টাকা
যেহেতু, Overtime এর প্রতিদিনের টাকার পরিমান নিয়মিত বেতন এর দ্বিগুন,
সেহেতু মোট overtime কাজ করার সময় = 480 ÷ (30×2) ঘন্টা = 8 ঘন্টা।

৪৫০.

If 30 men can do a piece of work in 20 hours, then in how many hours will 12 men do it?

ক
18 hours
খ
30 hours
গ
40 hours
ঘ
50 hours
ঙ
None of these

ব্যাখ্যা

Question: If 30 men can do a piece of work in 20 hours, then in how many hours will 12 men do it?

Solution:
As number of workers increase, the time required decreases. Hence, this is a problem related to indirect proportion.
Let the number of hours be x.
12 : 30 : : 20 : x
⇒ 12/30 = 20/x
⇒ x = (20 × 30)/12
∴ x = 50

12 men require 50 hours to complete the same work.

৪৫১.

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
ক) 9
খ
খ) 10
গ
গ) 11
ঘ
ঘ) 12
ঙ
ঙ) 15

ব্যাখ্যা

Let the required number of working hours per day be x.
More pumps , Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
Pumps 4 : 3 and Days 1 : 2 } :: 8:x
=> (4 × 1 × x) = (3 × 2 × 8)
=> x = 12

৪৫২.

A can do a certain job in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?

ক
ক) 7.2 days
খ
খ) 8 days
গ
গ) 7.5 days
ঘ
ঘ) 9 days

ব্যাখ্যা

Question: A can do a certain job in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?

Solution:
A completes one job in 12 days.
Hence the fraction of the job completed by A in 1 day =1/12

Since B is 60% more efficient than A,
Hence the fraction of the total job completed by B on one day =1/12 + 1/12 × (60/100)
= 1/12 + 1/20
= (5 + 3)/60
= 8/60
= 2/15

B can finish the job in 15/2 = 7.5 days

৪৫৩.

A man can do a work in 20 days and a woman in 15 days. If they work on it together for 5 days, then the fraction of the work that is left is-

ক
1/12
খ
1/10
গ
5/12
ঘ
7/15

ব্যাখ্যা

Question: A man can do a work in 20 days and a woman in 15 days. If they work on it together for 5 days, then the fraction of the work that is left is-

Solution:
Man’s 1 day’s work = 1/20
Woman’s 1 day’s work = 1/15

(Man + woman)’s 1 day’s work = (1/20 + 1/15) = 7/60
(Man + woman)’s 5 day’s work = (7/60 × 5) = 7/12

Thus, Remaining work = 1 - 7/12 = 5/12

৪৫৪.

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

ক
5 hours
খ
6 hours
গ
4 hours
ঘ
7 hours
ঙ
10 hours

ব্যাখ্যা

We are given that,
3 pumps, working 4 hours a day, can empty a tank in 2 days.
Therefore, it means that:
3 pumps take a total of 8 hours to empty the tank.
Hence, 1 pump will take 8 x 3 = 24 hours

As the number of pumps decreases, the time required increases.
So, if 4 pumps work, the time required decreases.
∴ 24/4 = 6hrs. needed to empty the tank in 1 day.

৪৫৫.

Two people start jogging at the same point and time but in opposite directions. If the rate of one jogger is 2 miles per hour faster than the other and after 3 hours, they are 30 miles apart. What is the rate of the faster jogger?

ক
ক) 3
খ
খ) 4
গ
গ) 5
ঘ
ঘ) 6

ব্যাখ্যা

মনেকরি,
প্রথম জনের গতিবেগ x মাইল/ঘণ্টা
দ্বিতীয় জনের গতিবেগ x + 2 মাইল/ঘণ্টা

প্রশ্নমতে,
3x + 3(x + 2) = 30
3x + 3x + 6 = 30
6x + 6 = 30
6x = 30 - 6
6x = 24
x = 4

দ্বিতীয় জনের গতিবেগ = 4 + 2 মাইল/ঘণ্টা
= 6 মাইল/ঘণ্টা

৪৫৬.

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

ক
7 hours
খ
8 hours
গ
6 hours
ঘ
5 hours
ঙ
None of these

ব্যাখ্যা

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

Solution:
As number of pumps increase, the time required decreases and when working hours increase, fewer days are required to complete the work. Hence, this is a problem related to indirect proportion.

More pumps (↑),Less working hours (↓)
More working hours (↑),Less days (↓)

⇒ 4 × 3 × 2 = 4 × 1 × x
⇒ 24 = 4x
∴ x = 6

৪৫৭.

Akib can do 1/6 of a work in 7 days. In how many days will he complete the work?

ক
36 days
খ
42 days
গ
46 days
ঘ
50 days

ব্যাখ্যা

Question: Akib can do 1/6 of a work in 7 days. In how many days will he complete the work?

Solution:
Akib can do 1/6 of a work in 7 days
∴ he will complete the work in (6 × 7) days
= 42 days

∴ Akib will complete the work in 42 days.

৪৫৮.

A fort had provision of food for 200 men for 60 days. After 20 days, 40 men left the fort. The number of days for which the remaining food will last, is-

ক
40 days
খ
50 days
গ
45 days
ঘ
55 days

ব্যাখ্যা

Question: A fort had provision of food for 200 men for 60 days. After 20 days, 40 men left the fort. The number of days for which the remaining food will last, is-

Solution:
After 20 days : 200 men had food for 40 days.
Suppose 160 men had food for x days.
Now, Less men, More days (Indirect Proportion)
160 : 200 : : 40 : x
⇒ 160/200 = 40/x
⇒ 160 x = 200 × 40
⇒ x = (200 × 40)/160
∴ x = 50 days

৪৫৯.

A wall 8 m long, 6 m high and 22.5 cm thick is made up of bricks, each measuring 25 cm × 11.25 cm × 6 cm. The number of bricks required is

ক
7,200
খ
6,400
গ
6,000
ঘ
5,600

ব্যাখ্যা

Question: A wall 8 m long, 6 m high and 22.5 cm thick is made up of bricks, each measuring 25 cm × 11.25 cm × 6 cm. The number of bricks required is

Solution:
দেয়ালের দৈর্ঘ্য l = 8m = 800cm
দেয়ালের উচ্চতা h = 6m = 600cm
দেয়ালের প্রস্থ b = 22.5cm

দেয়ালের আয়তন = lbh
=800 × 600 × 22.5
=10800000 cm3

ইটের দৈর্ঘ্য l = 25cm
ইটের প্রস্থ b = 11.25cm
ইটের উচ্চতা h = 6cm
ইটের আয়তন =lbh
=25 ×11.25 × 6
=1687.5cm3

ইটের সংখ্যা = 10800000/1687.5
= 6400 টি

৪৬০.

There is provision of food in fort for 1,200 soldiers for 60 days. After 15 days, 200 soldiers leave the fort. Remaining food will last for how many days.

ক
ক) 56 days
খ
খ) 50 days
গ
গ) 48 days
ঘ
ঘ) 54 days

ব্যাখ্যা

১৫ দিন পর সৈন্য আছে= (১২০০ - ২০০) জন = ১০০০ জন

১২০০ জন সৈন্যের খাবার আছে ৪৫ দিনের
১ জন সৈন্যের খাবার আছে ৪৫ ×১২০০ দিনের
১০০০ জন সৈন্যের খাবার আছে (৪৫ ×১২০০)/১০০০ দিনের
=৫৪ দিনের

৪৬১.

A, B and C completed a work costing Tk. 1800. A work for 6 days, B for 4 days and C for 9 days. If their daily wages are in the ratio of 5 : 6 : 4, how much amount will be received by A?

ক
ক) Tk. 420
খ
খ) Tk. 600
গ
গ) Tk. 750
ঘ
ঘ) Tk. 900

ব্যাখ্যা

Ratio of their daily wages = 5 : 6 : 4
Total wage = Tk. 1800
6 × 5x + 4 × 6x + 4 × 9x = 1800 [As A, B, C works for 6, 4, 9 days respectively]
Or, 90x = 1800
Or, x = 1800/90

Total amount of A
= 1800 × 30/90
= Tk. 600

৪৬২.

A and B can do a piece of work in 40 days, B and C can do it in 120 days. If B alone can do it in 180 days, in how many days will A and C do it together?

ক
18 days
খ
25 days
গ
22.5 days
ঘ
45 days

ব্যাখ্যা

Question: A and B can do a piece of work in 40 days, B and C can do it in 120 days. If B alone can do it in 180 days, in how many days will A and C do it together?

Solution:
A + B take 40 days. B alone takes 180 days.
∴ A will take 1/40 - 1/180 = 7/360 i.e. 360/7 days.

B + C take 120 days.
∴ C alone will take 1/120 - 1/180 = 1/360 360 days.

∴ A & C together will take 7/360 + 1/360 = 8/360 i.e. 360/8 = 45 days to complete the work.

৪৬৩.

X can do 1/5 of a work in 8 days, Y can do 25% of the work in 50 days and Z can do 1/4 of the work in 15 days. Who will complete the work first?

ক
X
খ
Y
গ
Z
ঘ
X and Y both
ঙ
None of these

ব্যাখ্যা

Question: X can do 1/5 of a work in 8 days, Y can do 25% of the work in 50 days and Z can do 1/4 of the work in 15 days. Who will complete the work first?

Solution:
X এর সম্পূর্ণ কাজ করতে সময় লাগবে = (5 × 8) = 40 দিন

Y এর সম্পূর্ণ কাজ করতে সময় লাগবে = {50 × (100/25)} = 200 দিন

Z এর সম্পূর্ণ কাজ করতে সময় লাগবে = (4 × 15) = 60 দিন

∴ X পুরো কাজ সবচেয়ে কম সময়ে, অর্থাৎ 40 দিনে শেষ করতে পারবে।

৪৬৪.

A tank has water for 72 trees and can last for 54 days for them. If each tree is given 10% less water than 90 trees can get the water for how many days?

ক
ক) 24 days
খ
খ) 36 days
গ
গ) 42 days
ঘ
ঘ) 48 days

ব্যাখ্যা

Let each tree take T amount of water every day.
So 72 trees take 72T water in one day.

With 10% reduction each tree will consume 90T/100 amount each day.
So 90 trees take 90 (90T/100) amount in one day
Total water quantity is constant
∴ 72T × 54 = 90 × (90T/100) × D
∴ D = 48 days = Number of days 90 trees can use the water.

৪৬৫.

After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?

ক
ক) 20
খ
খ) 8
গ
গ) 5
ঘ
ঘ) 3.2

ব্যাখ্যা

প্রশ্ন: After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?

সমাধান:
প্রতি ড্রপে বলটি পূর্ববর্তী উচ্চতার ২/৫ অংশ উঠে।

১ম ড্রপে বলটি উঠে ১২৫ ইঞ্চি

২য় ড্রপে বলটি উঠে {১২৫ × (২/৫)} ইঞ্চি
= ৫০ ইঞ্চি

৩য় ড্রপে বলটি উঠে {৫০ × (২/৫)} ইঞ্চি
= ২০ ইঞ্চি

৪র্থ ড্রপে বলটি উঠে { ২০ × (২/৫)} ইঞ্চি
= ৮ ইঞ্চি

৪৬৬.

Rene earns Tk. 85 per hour on days other than Sundays and twice that rate on Sundays. Last week she worked a total of 40 hours, including 8 hours on Sunday. What were her earnings for the week?

ক
Tk. 2720
খ
Tk. 3400
গ
Tk. 3980
ঘ
Tk. 4080
ঙ
Tk. 4760

ব্যাখ্যা

Question: Rene earns Tk. 85 per hour on days other than Sundays and twice that rate on Sundays. Last week she worked a total of 40 hours, including 8 hours on Sunday. What were her earnings for the week?

Solution:
During the week Rene worked a total of 40 - 8 = 32 hours at a rate of Tk. 85 per hour.
On Sunday she worked 8 hours at a rate of Tk. 85 × 2 = Tk. 170 per hour.

Therefore her total earnings for the week were 32 × 85 + 8 × 170 = Tk. 4080

৪৬৭.

If the daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.

ক
12
খ
14
গ
18
ঘ
16

ব্যাখ্যা

Wages of 1 woman for 1 day = 21600/(40 × 30)
Wages of 1 man for 1 day = (21600 × 2)/(40 × 30)
Wages of 1 man for 25 days = (21600 × 2 × 25)/(40 × 30)
Number of men = 14400/{(21600 × 2 × 25)/(40 × 30)}
= 144/{(216 × 50)/(40 × 30)}
= 144/9
= 16.

৪৬৮.

If 45 students can consume a stock of food in 2 months, then for how many days the same stock of food will last for 27 students?

ক
100 days
খ
144 days
গ
160 days
ঘ
180 days

ব্যাখ্যা

Question: If 45 students can consume a stock of food in 2 months, then for how many days the same stock of food will last for 27 students?

Solution:
According to the first condition, students consume food in 2 months, i.e. in 60 days.
So this ratio would be 45 : 60

According to the second condition, the same amount of food is consumed by 27 students in x days.
So that ratio would be 27 : x.

By Inverse Proportion,
45 × 60 = 27 × x
⇒ x = (45 × 60) / 27
∴ x = 100

৪৬৯.

দুটি মেশিন এক সাথে ঘণ্টায় 4টি খেলনা তৈরী করে। 6টি মেশিন 2 ঘণ্টায় কতটি খেলনা তৈরী করবে?

ক
32
খ
16
গ
12
ঘ
24

ব্যাখ্যা

প্রশ্ন: দুটি মেশিন এক সাথে ঘণ্টায় 4টি খেলনা তৈরী করে। 6টি মেশিন 2 ঘণ্টায় কতটি খেলনা তৈরী করবে?

সমাধান;
2 টি মেশিন 1 ঘণ্টায় তৈরী করে = 4 টি খেলনা
∴ 1 টি মেশিন 1 ঘণ্টায় তৈরী করে = 4/2 টি খেলনা
∴ 6 টি মেশিন 1 ঘণ্টায় তৈরী করে = (4 × 6)/2 টি খেলনা
∴ 6 টি মেশিন 2 ঘণ্টায় তৈরী করে = (4 × 6 × 2)/2 টি খেলনা
= 24 টি খেলনা

৪৭০.

In a factory, 20 people can make 20 toys in 15 days working 10 hours per day. Then, in how many days can 25 persons make 30 toys working 20 hours per day?

ক
6 days
খ
15 days
গ
12 days
ঘ
9 days

ব্যাখ্যা

Question: In a factory, 20 people can make 20 toys in 15 days working 10 hours per day. Then, in how many days can 25 persons make 30 toys working 20 hours per day?

Solution:
Here,
M₁ = 20, M₂ = 25
D₁ = 15, D₂ = ?
T₁ = 10, T₂ = 20,
W₁ = 20 and W₂ = 30.

We know,
M₁ × D₁ × T₁ × W₂ = M₂ × D₂ × T₂ × W₁
⇒ 20 × 15 × 10 × 30 = 25 × D₂ × 20 × 20
∴ D₂ = 9

Thus, the required day = 9 days

৪৭১.

If 25 men can build a wall 70 meters long in 6 days, what length of a similar wall can be built by 35 men in 3 days?

ক
39 meters
খ
42 meters
গ
46 meters
ঘ
49 meters

ব্যাখ্যা

Question: If 25 men can build a wall 70 meters long in 6 days, what length of a similar wall can be built by 35 men in 3 days?

Solution:
In 6 days 25 men can build 70 meters
∴ In 1 day 1 man can build 70/(6 × 25) meters.
∴ In 3 days 35 men can build (70 × 35 × 3)/(6 × 25) meters.
= 49 meters.

৪৭২.

A water pump fills a tank in 8 hours. If two identical pumps work together, how long will it take to fill the same tank?

ক
2 hours
খ
6 hours
গ
8 hours
ঘ
None above

ব্যাখ্যা

Question: A water pump fills a tank in 8 hours. If two identical pumps work together, how long will it take to fill the same tank?

Solution:
One pump fills the tank in 8 hours.
Rate of one pump = 1/8 per hour

If two identical pumps work together, their rates add up.
So, the combined rate is = 1/8 + 1/8
= 1/4 per hour

∴ Time = 1/(1/4) = 4 hours

৪৭৩.

P can do a piece of work in 4 hours, Q and R together in 3 hours, and P and R together in 2 hours. How long will Q alone take to do it?

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

ব্যাখ্যা

Question: P can do a piece of work in 4 hours, Q and R together in 3 hours, and P and R together in 2 hours. How long will Q alone take to do it?

Solution:
P's 1 hour's work = 1/4
(Q + R)'s 1 hour's work = 1/3
(P + R)'s 1 hour's work = 1/2

∴ R's 1 hour's work = (1/2) - (1/4) = 1/4

Q's 1 hour's work = (1/3) - (1/4) = 1/12

Hence, Q will complete the whole work in 12 hours.

৪৭৪.

If 40 workers can construct a road in 30 days, how many workers are needed to construct the same road in 20 days?

ক
70
খ
50
গ
60
ঘ
55
ঙ
65

ব্যাখ্যা

Question: If 40 workers can construct a road in 30 days, how many workers are needed to construct the same road in 20 days?

Solution:
Here,
M₁ = 40, M₂ = ?, D₁ = 30, D₂ = 20

∴ (M₁ × D₁) = (M₂ × D₂)
⇒ (40 × 30) = (20 × M₂)
⇒ M₂ = (40 × 30)/20
⇒ M₂ = 60

So 60 workers are needed to construct the same road in 20 days.

৪৭৫.

If a person cycles at 18 km/h instead of 12 km/h, he would have covered 24 km more. What is the actual distance he travelled?

ক
56 km
খ
54 km
গ
50 km
ঘ
48 km
ঙ
None of these

ব্যাখ্যা

Question: If a person cycles at 18 km/h instead of 12 km/h, he would have covered 24 km more. What is the actual distance he travelled?

Solution:
Let
the actual distance he travelled be x km.

ATQ,
x/12 = (x + 24)/18
⇒ 18x = 12x + 288
⇒ 6x = 288
∴ x = 48

৪৭৬.

P and Q can do a job in 3 days. Q and R can do the same job in 4 days, while R and P can do it in 12 days. In how many days the job will be finished when P, Q and R working together.

ক
10 days
খ
3 days
গ
4 days
ঘ
12 days

ব্যাখ্যা

Question: P and Q can do a job in 3 days. Q and R can do the same job in 4 days, while R and P can do it in 12 days. In how many days the job will be finished when P, Q and R working together.

Solution:
Given that,
(P + Q)'s 1 day's work = 1/3
(Q + R )'s 1 day's work= 1/4
and
(R + P)'s 1 day's work = 1/12

Now, (P + Q) + (Q + R) + (R + P) = 2(P + Q + R)'s 1 day's work = (1/3) + (1/4) + (1/12)
= (4 + 3 + 1)/12
= 8/12 = 2/3
∴ (P + Q + R)'s 1 day's work = 2/(3 × 2) = 1/3

So, P + Q + R can complete the job in = 3 days

৪৭৭.

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
18 hours
খ
15 hours
গ
9 hours
ঘ
12 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, working 8 hours a day, can empty a tank in 2 days
Formula used: M₁ × T₁ = M₂ × T₂
Where M₁ and M₂ is men and T₁ and T₂ is time

Calculation:
Let H hours be the number of hours required Applying the above formula
⇒ 3 × 8 × 2 = 4 × 1 × H
⇒ H = 48/4
⇒ H = 12 hours

∴ 4 pump need to work 12 hours to complete the work in 1 day.

৪৭৮.

A does half as much work as B in one-sixth of the time. If together they take 15 days to complete a work, how much time shall B alone take to do it?

ক
ক) 30 days
খ
খ) 45 days
গ
গ) 60 days
ঘ
ঘ) 75 days

ব্যাখ্যা

Question: A does half as much work as B in one-sixth of the time. If together they take 15 days to complete a work, how much time shall B alone take to do it?

Solution:
Let B takes x days to do the work.
A takes 1/6 of x time to do 1/2 of the work.
∴ the work will be dy by A in (x/6) × 2 days
= x/3 days

ATQ,
1/x + 3/x = 1/15
⇒ 4/x = 1/15
⇒ x = 60

৪৭৯.

If 3 men or 9 boys can do a job in 60 days, how long will it take 11 men and 27 boys to finish the same job?

ক
6 days
খ
9 days
গ
10 days
ঘ
12 days

ব্যাখ্যা

Question: If 3 men or 9 boys can do a job in 60 days, how long will it take 11 men and 27 boys to finish the same job?

Solution:
9 জন বালক = 3 জন পুরুষ

1 জন বালক = 3/9 = 1/3 জন পুরুষ
∴ 27 জন বালক = 27/3 = 9 জন পুরুষ

11 জন পুরুষ + 27 জন বালক = (11 + 9) = 20 জন পুরুষ

3 জন পুরুষ কাজটি করতে সময় নেয় = 60 দিন
∴ 1 জন পুরুষ কাজটি করতে সময় নেয় = (60 × 3) দিন
∴ 20 জন পুরুষ কাজটি করতে সময় নেয় = (60 × 3)/20 = 9 দিন

৪৮০.

'A' can do a work in 12 days, and 'B' in 24 days. They work together for 6 days. How much of the work is left?

ক
1/2
খ
1/4
গ
2/3
ঘ
5/8

ব্যাখ্যা

Question: 'A' can do a work in 12 days, and 'B' in 24 days. They work together for 6 days. How much of the work is left?

সমাধান:
মনে করি,
সম্পূর্ণ কাজ = 1 অংশ

∴ A একা একদিনে করে = 1/12 অংশ।
B একা একদিনে করে = 1/24 অংশ।

∴ A ও B একসাথে একদিনে করে = (1/12) + (1/24) অংশ
= (2 + 1)/24
= 3/24
= 1/8 অংশ

∴ A ও B একসাথে 6 দিনে করে = 6 × (1/8) অংশ
= 3/4 অংশ

∴ কাজ বাকি থাকে = 1 - (3/4) অংশ
= (4 - 3)/4
= 1/4 অংশ

৪৮১.

A, B and C start together from the same place to walk round a circular path of length 12km. A walks at the rate of 6 km/h, B 3 km/h and C 3/2 km/h. They will meet together at the starting place at the end of-

ক
8 hours
খ
9 hours
গ
9.5 hours
ঘ
10 hours

ব্যাখ্যা

Question: A, B and C start together from the same place to walk round a circular path of length 12km. A walks at the rate of 6 km/h, B 3 km/h and C 3/2 km/h. They will meet together at the starting place at the end of-

Solution:
We know,
Time = Distance/speed

Time taken to complete the revolution
A = 12/6 = 2 hours
B = 12/3 = 4 hours
C = 12 × (2/3) = 8 hours

Now, required time = LCM of 2, 4, and 8
= 8 hours

৪৮২.

An employee may claim Tk. 7 for each kilometer when he travels by taxi and Tk. 6 for each kilometer when he drives his own car. If in one week he claimed Tk. 900 for travelling 135 km, how many kilometers did he drive his own car?

ক
90 km
খ
75 km
গ
55 km
ঘ
45 km

ব্যাখ্যা

Question: An employee may claim Tk. 7 for each kilometer when he travels by taxi and Tk. 6 for each kilometer when he drives his own car. If in one week he claimed Tk. 900 for travelling 135 km, how many kilometers did he drive his own car?

Solution:
Let,
The distance travelled by taxi x km
The distance travelled by own car 135 - x km

Now,
7x + 6(135 - x) = 900
⇒ 7x + 810 - 6x = 900
⇒ x + 810 = 900
⇒ x = 900 - 810
∴ x = 90

∴ The distance travelled by own car 135 - 90 = 45 km

৪৮৩.

A is thrice as good a workman as B and so takes 40 days less than B for doing a job. The time in which they can do the job together is -

ক
ক) 20 days
খ
খ) 15 days
গ
গ) 30 days
ঘ
ঘ) 24 days

ব্যাখ্যা

Question: A is thrice as good a workman as B and so takes 40 days less than B for doing a job. The time in which they can do the job together is -

Solution:
Let A alone takes x days
and B alone takes 3x days to complete the job.

ATQ,
3x - x = 40
⇒ 2x = 40
⇒ x = 20

So, A alone takes 20 days and B alone takes 3 × 20 = 60 days to complete the job.

(A + B)'s 1 days work = (1/20 + 1/60) = 1/15 part

∴ A and B together can do the work in 15 days.

৪৮৪.

While working 8 hours a day, A alone can complete a piece of work in 8 days and B alone in 10 days. At what time would they complete it together, 5 hours a day?

ক
128/9 days
খ
7 days
গ
55/9 days
ঘ
64/9 days

ব্যাখ্যা

Question: While working 8 hours a day, A alone can complete a piece of work in 8 days and B alone in 10 days. In what time would they complete it together, 5 hours a day?

Solution:
A can complete the work in 8 × 8 = 64 hours
1 hour's work of A = 1/64

B can complete the work in 10 × 8 = 80 hours
1 hour's work of B = 1/80

(A + B)'s 1 hour's work
= 1/64 + 1/80
= (5 + 4)/320
= 9/320

they can complete the work in = 320/9 hours

∴ as they will work 5 hours a day, it will take = 320/(9 × 5) = 64/9 days

৪৮৫.

Pervez and Sunny can complete a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which Sunny was replaced by Ashu. If the work would be finished in next 4 days, find the number of days in which Ashu alone could complete the work.

ক
36
খ
40
গ
45
ঘ
56

ব্যাখ্যা

Question: Pervez and Sunny can complete a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which Sunny was replaced by Ashu. If the work would be finished in next 4 days, find the number of days in which Ashu alone could complete the work.

Solution:
Pervez can complete the work in 20 days
Sunny can complete the same job in 15 days
Let the total work = LCM of both
Therefore, the LCM of 20 and 15 is 60, that means total work = 60 units
Now, Pervez's one-day work efficiency = 60/20 = 3 units
Sunny's one-day work efficiency = 60/15 = 4 units
ATQ,
(Pervez + Sunny) together works for 6 days
That means (Pervez+Sunny) have done 7 × 6 = 42 units work in 6 days
Now, the remaining work will be 60 - 42 = 18 units, and it will finish in 4 days.
Now, Sunny is replaced with Ashu:
So, per days work required to be finished = 18 units / 4 days = 4.5 units
But, we know that Pervez's one-day work = 3 units, so Ashu's one-day work = 4.5 - 3 = 1.5 units
Therefore, Ashu alone can finish the total work in 60 units /1.5 days = 40 days

৪৮৬.

If X and Y can complete a work together in 12 days, Y and Z together in 20 days, and X and Z together in 15 days, then in how many days can Y alone complete the work?

ক
24 days
খ
30 days
গ
36 days
ঘ
40 days

ব্যাখ্যা

Question: If X and Y can complete a work together in 12 days, Y and Z together in 20 days, and X and Z together in 15 days, then in how many days can Y alone complete the work?

Solution:
মনে করি, সম্পূর্ণ কাজ = 1 অংশ

∴ (X + Y) একদিনে করে = 1/12 অংশ ..........(1)
(Y + Z) একদিনে করে = 1/20 অংশ ..........(2)
(X + Z) একদিনে করে = 1/15 অংশ ..........(3)

(1), (2), (3) যোগ করে পাই,
2 × (X + Y + Z) = (1/12) + (1/20) + (1/15)
⇒ 2 × (X + Y + Z) = (5 + 3 + 4)/60 = 12/60
⇒ 2 × (X + Y + Z) = 1/5
⇒ (X + Y + Z) = 1/10

∴ X, Y এবং Z একসাথে একদিনে করে = 1/10 অংশ

(X + Z) একসাথে একদিনে করে = 1/15 অংশ
∴ Y-এর একদিনের কাজ = (1/10) - (1/15) অংশ
= (3 - 2)/30
= 1/30

অর্থাৎ, Y সম্পূর্ণ কাজ করে = 1 ÷ (1/30) = 30 দিনে

৪৮৭.

If 500 laborers can complete a work in 48 days, determine the number of extra laborers required to finish the same work in 40 days.

ক
60
খ
80
গ
100
ঘ
120

ব্যাখ্যা

Question: If 500 laborers can complete a work in 48 days, determine the number of extra laborers required to finish the same work in 40 days.

Solution:
48 দিনে কাজটি করতে শ্রমিক লাগে = 500 জন
∴ 1 দিনে কাজটি করতে শ্রমিক লাগে = (500 × 48) জন লোক
∴ 40 দিনে কাজটি করতে শ্রমিক লাগে = (500 × 48)/40 জন
= 600 জন

∴ অতিরিক্ত শ্রমিক লাগবে = (600 - 500) জন = 100 জন

৪৮৮.

If a quarter kg of potato costs 25 Tk. How much Tk. will 200 gm cost?

ক
ক) 15 Tk.
খ
খ) 20 Tk.
গ
গ) 22 Tk.
ঘ
ঘ) 25 Tk.

ব্যাখ্যা

Question: If a quarter kg of potato costs 25 Tk. How much Tk. will 200 gm cost?

Solution:
a quarter of kg means 250gm

so,
250gm costs 25 Tk.
∴200gm costa (200 × 25)/250 Tk.
= 20 Tk.

৪৮৯.

Distribution of work House in a Factory

The number of workers who worked from 40 to 44 hours is x times the number who worked up to 34 hours. Where x is?

ক
ক) 4
খ
খ) 5
গ
গ) 1.33
ঘ
ঘ) 3/4

ব্যাখ্যা

Question: Distribution of work House in a Factory

The number of workers who worked from 40 to 44 hours is x times the number who worked up to 34 hours. Where x is?

Solution:
In a week 15 workers do the job for 40 to 44 hours.
4 + 16 = 20 workers do the job for 0 to 34 hours.

∴ x = 15/20 = 3/4

৪৯০.

3 men can build a stage in 18 days while 6 boys can also do it in 18 days. If 4 men and 4 boys work on the assignment together, how many days will they take to finish it?

ক
ক) 4.5 days
খ
খ) 6 days
গ
গ) 9 days
ঘ
ঘ) 27 days

ব্যাখ্যা

To complete work in 18 days we need either 3 men or 6 boys.
∴ 1 man = 2 boys
Take work done = 1
∴ 3 men x 18 days x 1 = (4 men + 4 boys) x ? days x 1
∴ 6 boys x 18 days x 1 = (8 boys + 4 boys) x ? days x 1 [Convert either all men to boys or all boys to men.]
∴ ? = 9 days = they will need these many days.

৪৯১.

A time-study specialist has set the production rate for each worker on a certain job at 22 units every 3 hours. At this rate what is the minimum number of workers that should be put on the job if at least 90 units are to be produced per hour?

ক
ক) 12
খ
খ) 13
গ
গ) 18
ঘ
ঘ) 30
ঙ
ঙ) None of these

ব্যাখ্যা

১ জন কর্মী ৩ ঘণ্টায় কাজ করলে ২২ ইউনিট উৎপাদন করে। তাহলে ১ জন ১ ঘণ্টায় করে ২২/৩ ইউনিট। তাহলে ৯০ ইউনিট ১ ঘণ্টায় করতে কর্মী লাগবে ৯০ / (২২/৩) = ১২.২৭ ≅ ১৩ জন।

৪৯২.

Titu, Pintu and Mithu can complete a piece of work in 18, 6 and 12 days respectively. Working together, they will complete the same work in:

ক
ক) 36/5 days
খ
খ) 36/7 days
গ
গ) 36/13 days
ঘ
ঘ) 36/11 days

ব্যাখ্যা

(Titu + Pintu + Mithu)'s 1 day's work =(1/18) + (1/6) + (1/12)
=(2 + 6 + 3)/36
= 11/36

All the three together will complete the job in 36/11 days

৪৯৩.

A is thrice as good a workman as B and so takes 40 days less than B for doing a job. The time in which they can do the job together is-

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

ব্যাখ্যা

Question: A is thrice as good a workman as B and so takes 40 days less than B for doing a job. The time in which they can do the job together is-

Solution:
Let, A alone takes x days and B alone takes 3x days to complete the work.

According to the question,
3x - x = 40
⇒ 2x = 40
⇒ x = 20

So, A takes 20 days and B takes ( 3 × 20) = 60 days

Now, ( A+B )'s 1 days work = (1/20) + (1/60)
= 4/60
= 1/15

∴ A & B together can do the work in 15 days.

৪৯৪.

Zisan completed the school project in 20 days. How many days will Ali take to complete the same work if he is 25% more efficient than Zisan?

ক
12 days
খ
14 days
গ
16 days
ঘ
18 days

ব্যাখ্যা

প্রশ্ন: Zisan completed the school project in 20 days. How many days will Ali take to complete the same work if he is 25% more efficient than Zisan?

সমাধান:
আলী জিসানের চেয়ে ২৫% দক্ষ।

অর্থাৎ,
জিসান ১২৫ দিন সময় নিলে আলী নিবে ১০০ দিন
∴ জিসান ১ দিন সময় নিলে আলী নিবে ১০০/১২৫ দিন
∴ জিসান ২০ দিন সময় নিলে আলী নিবে (১০০ × ২০)/১২৫ দিন
= ১৬ দিন

৪৯৫.

A and B working together can finish a work in 12 days, B and C working together can finish the work in 16 days. If A works for 5 days, B works for 7 days, and C completes the remaining work in 11 days, C alone can complete the work in how many days?

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

ব্যাখ্যা

Question: A and B working together can finish a work in 12 days, B and C working together can finish the work in 16 days. If A works for 5 days, B works for 7 days, and C completes the remaining work in 11 days, C alone can complete the work in how many days?

Solution:
ATQ,
A + B = 12 days
B + C = 16 days

Note: Assume the total work = LCM of the given days
Take the LCM of days = LCM of (12 and 16) = 48
Let the total work = 48

Note: One day work = (total work/ days)
Now,
(A + B)'s one day work = 48/12 = 4 unit
(B + C)'s one day work = 48/16 = 3 unit

As per the question:
A works for 5 days
B works for 7 days or (5 + 2) days, that means B works 5 days with A and remaining 2 days with C.
C works 13 days or (2 + 11) days, that means C works 2 days with B and remaining 11 days alone.

That means total work done by (A + B) in 5 days
A + B = 5 days × 4 unit = 20 units
And, total work done by (B + C) = 2 days × 3 unit = 6 units
So, A + B + C finish the 26 units of work.

Remaining work = 48 - 26 = 22 unit work
And C completes the remaining work in 11 days.
i.e., C's one day's works = 22/11 = 2 units.

C alone can finish total work in [total work/ C's one day work] = [48/2] = 24 days.

৪৯৬.

A wheel rotates 10 times per minute and moves 20 m during each rotation. How many meters does the wheel move in 1 hour?

ক
ক) 10000
খ
খ) 20000
গ
গ) 18000
ঘ
ঘ) 12000

ব্যাখ্যা

Number of rotation in one hour = 10 × 60 = 600
So, Distance moved = (600 × 20) = 12000 m

৪৯৭.

12 workers can dig a 36-meter long trench working 8 hours per day. How many extra workers are required to dig a 45-meter long trench working 5 hours per day?

ক
6 workers
খ
0 workers
গ
10 workers
ঘ
12 workers

ব্যাখ্যা

Question: 12 workers can dig a 36-meter long trench working 8 hours per day. How many extra workers are required to dig a 45-meter long trench working 5 hours per day?

Solution:
8 ঘণ্টা কাজ করে 36 মিটার পরিখা খনন করে 12 জন শ্রমিক।
1 ঘণ্টা কাজ করে 1 মিটার পরিখা খনন করতে প্রয়োজন = (12 × 8)/36 জন শ্রমিক
5 ঘণ্টা কাজ করে 45 মিটার পরিখা খনন করতে প্রয়োজন = (12 × 8 × 45)/(36 × 5) জন শ্রমিক
= (12 × 8 × 45)/180 জন শ্রমিক
= 4320/180 জন শ্রমিক
= 24 জন শ্রমিক

∴ অতিরিক্ত শ্রমিকের সংখ্যা = 24 - 12 = 12 জন

৪৯৮.

At 7 : 15, how many degrees are included between hands of hour and minute of the clock?

ক
62.5°
খ
95°
গ
115°
ঘ
127.5°

ব্যাখ্যা

Question: At 7 : 15, how many degrees are included between hands of hour and minute of the clock?

Solution:
Value of angle = {(11 × 15) - (60 × 7)}/2
= (165 - 420)/2
= 255/2
= 127.5°

৪৯৯.

In a camp, meals are prepared for 120 men or 200 children. If 150 children have already eaten, how many men can be served with the leftover food?

ক
20 men
খ
40 men
গ
30 men
ঘ
45 men

ব্যাখ্যা

Question: In a camp, meals are prepared for 120 men or 200 children. If 150 children have already eaten, how many men can be served with the leftover food?

Solution:
Camp has = 200 children
Already have taken meal = 150 children

Remaining children to take meal = 200 - 150 = 50 children

The camp has meal for 200 children = 120 men
The camp has meal for 1 children = 120/200 men
The camp has meal for 50 children = (120 × 50)/200 men
= 30 men

৫০০.

Piyal and Belal together can complete a work in 3 days. They start together but after 2 days, Belal left the work. If the work is completed after two more days, Belal alone could do the work in how many days?

ক
3 days
খ
4 days
গ
5 days
ঘ
6 days

ব্যাখ্যা

Question: Piyal and Belal together can complete a work in 3 days. They start together but after 2 days, Belal left the work. If the work is completed after two more days, Belal alone could do the work in how many days?

Solution:
(Piyal + Belal)'s one day's work = 1/3 part
(Piyal + Belal) works 2 days together = 2/3 part
Remaining work = 1- 2/3
= 1/3 part

1/3 part of work is completed by Piyal in two days
Hence, one day's work of Piyal = 1/6 part

Then, one day's work of Belal = 1/3 - 1/6 = 1/6
So, Belal alone can complete the whole work in 6 days.