লগ ইননিবন্ধন
পরীক্ষা আর্কাইভ

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়45 minutes
মোট প্রশ্ন২৫
সিলেবাস
Math - 05 - Time & Work, Chain Rule
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২৫ প্রশ্ন

১.
20 women take 20 minutes to roll 20 breads. How many breads can 400 women roll in 400 minutes?
  1. ক
    ক) 20
  2. খ
    খ) 2000
  3. গ
    গ) 4000
  4. ঘ
    ঘ) 8000
ব্যাখ্যা

Men = M; Days = D; Time/Hours = T; Work = W
M1D1T1W2 = M2D2T2W1
Note that W2 is on left side and W1 is on right side

∴ 20 women x 20 minutes x ? = 400 women x 400 minutes x 20 chapattis
∴ ? = 8000 breads = Are rolled by 400 women in 400 minutes.

২.
A ship was stocked with food to last for 40 days for 2500 sailors. However, some sailors could not board the ship and the food could last for 50 days. How many sailors could not board the ship?
  1. ক
    ক) 400
  2. খ
    খ) 500
  3. গ
    গ) 700
  4. ঘ
    ঘ) 1000
ব্যাখ্যা

Take work done = 1
Let number of sailors who could not board = S.
So sailors who boarded = 2500 - S
∴ 2500 sailors x 40 days x 1 = (2500 - S) sailors x 50 days x 1
∴ S = 500 = Sailors who could not board the ship.

[Men = M; Days = D; Time/Hours = T; Work = W
M1D1T1W2 = M2D2T2W1
Note that - W2 is on left side and W1 is on right side]

৩.
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?
  1. ক
    ক) 4.5 days
  2. খ
    খ) 6 days
  3. গ
    গ) 9 days
  4. 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.

৪.
75 employees have been able to finish only one-third of the project in 40 hours. The time committed by the management to complete the project was 90 hours. How many more employees should join the team to complete the project on time?
  1. ক
    ক) 45
  2. খ
    খ) 55
  3. গ
    গ) 100
  4. ঘ
    ঘ) 150
ব্যাখ্যা

Remaining work = 1 - (1/3) = 2/3
Let number of more employees needed be E
Thus (75+E) employees complete 2/3 works in 50 hours.
∴ 75 employes × 40 hours × (2/3) = (75 + E) × 50 hours × (1/3)
∴ E = 45 = these many more employees are needed.

৫.
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?
  1. ক
    ক) 24 days
  2. খ
    খ) 36 days
  3. গ
    গ) 42 days
  4. 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.

৬.
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?
  1. ক
    ক) 7/15 times more efficient
  2. খ
    খ) 7/12 times more efficient
  3. গ
    গ) 3/4 times more efficient
  4. 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.

৭.
No. of books bound by a child is half the number of books a man can bind. 20 men and 16 children take 10 days to bind all the books. If there are 8 men and 12 children working on the assignment, how many days will they take to bind all the books?
  1. ক
    ক) 20 days
  2. খ
    খ) 24 days
  3. গ
    গ) 25 days
  4. ঘ
    ঘ) 40 days
ব্যাখ্যা

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

1 child binds half the number of books bound by 1 adult
∴ 1 adult = 2 children
Take work done = 1
∴ (20 adults + 16 children) x 10 days x 1 = (8 adults + 12 children) x ? days x 1
∴ 56 children x 10 days x 1 = 28 children x ? days x 1 [Convert either all adults to children or all children to adults.]
∴ ? = 20 days = they will need these many days.

৮.
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?
  1. ক
    ক) 13 days
  2. খ
    খ) 36 days
  3. গ
    গ) 52 days
  4. 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.

৯.
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?
  1. ক
    ক) 7 hours
  2. খ
    খ) 8 hours
  3. গ
    গ) 6 hours
  4. ঘ
    ঘ) 5 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.

১০.
In a dairy farm, 20 cows eat 20 bags in 20 days. In how many days one cow will eat one bag of husk?
  1. ক
    ক) 10 days
  2. খ
    খ) 1/10 days
  3. গ
    গ) 20 days
  4. 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.

১১.
A hostel had provisions for 250 men for 40 days. If 50 men left the hostel, how long will the food last at the same rate?
  1. ক
    ক) 45 days
  2. খ
    খ) 48 days
  3. গ
    গ) 50 days
  4. ঘ
    ঘ) 60 days
ব্যাখ্যা

A hostel had provisions for 250 men for 40 days

If 50 men leaves the hostel, remaining men = 250 - 50 = 200
We need to find out how long the food will last for these 200 men.

Let the required number of days = x days.

More men, Less days (Indirect Proportion)
(men) 250 : 200 :: x : 40
⇒ 250 × 40 = 200x
⇒ 5 × 40 = 4x
⇒ x = 5 × 10
= 50

১২.
In a camp, food was sufficient for 2000 people for 54 days. After 15 days, more people came and the food lasted only for 20 more days. How many people came?
  1. ক
    ক) 1900
  2. খ
    খ) 1800
  3. গ
    গ) 2000
  4. ঘ
    ঘ) 1940
ব্যাখ্যা

Given that food was sufficient for 2000 people for 54 days
Hence, after 15 days, the remaining food was sufficient for 2000 people for 39 days (∵ 54 - 15 = 39)

Let x number of people come after 15 days.
Then, total number of people after 15 days = (2000 + x)
Then, the remaining food was sufficient for (2000 + x) people for 20 days

More men, Less days (Indirect Proportion)

(men) 2000 : (2000 + x) :: 20 : 39
⇒ 2000 × 39 = (2000 + x) 20
⇒ 100 × 39 = (2000 + x)
⇒ 3900 = 2000 + x
⇒ x = 3900 − 2000
= 1900

১৩.
A rope can make 70 rounds of the circumference of a cylinder whose radius of the base is 14cm. How many times can it go round a cylinder having radius 20 cm?
  1. ক
    ক) 54 rounds
  2. খ
    খ) 42 rounds
  3. গ
    গ) 49 rounds
  4. ঘ
    ঘ) 52 rounds
ব্যাখ্যা

Let the required number of rounds be x

More radius, less rounds(Indirect proportion)

Hence we can write as
(radius) 14 : 20 :: x : 70
⇒ 14 × 70 = 20x
⇒ 14 × 7 = 2x
⇒ x = 7 × 7
= 49 days.

১৪.
Akash are 5 times as efficient as Biplob. Akash can finish the work 60 days earlier than Biplob. If they work individually, how many days would they take to finish the work?
  1. ক
    ক) Akash = 10 days; Biplob = 50 days
  2. খ
    খ) Akash = 15 days; Biplob = 75 days
  3. গ
    গ) Akash = 20 days; Biplob = 80 days
  4. ঘ
    ঘ) Akash = 20 days; Biplob = 100 days
ব্যাখ্যা

We know,
Speed of Work / Efficiency ∝ 1/Time needed
So more the efficiency, less time is needed to do the task.

Let us denote Akash by 'A' and Biplob by 'B'
Hence,
if A is 5 times faster than B, then B needs 5 times more time than A.
Let A need 'n' days to complete the work.
So B will need 5n days.
Also, 5n – n = 60 ------------------- Given
∴ n = 15 days = Days needed by A to complete work individually
Days needed by B to complete work individually = 5n = 5 x 15 = 75 days.

১৫.
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.
  1. ক
    ক) 3 days
  2. খ
    খ) 6 days
  3. গ
    গ) 7.5 days
  4. 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.]

১৬.
Working individually, A would finish a project in 3 days. B takes double the time as taken by A, C takes one more day in addition to the time taken by B. If all three of them decide to work together on the project, how much time would they take to finish it?
  1. ক
    ক) 15/16 days
  2. খ
    খ) 11/10 days
  3. গ
    গ) 14/9 days
  4. ঘ
    ঘ) 16/7 days
ব্যাখ্যা

A can do the work in 3 days. So, in 1 day a does 1/3 amount of work.

B takes double the time as A. So, B can do the work in 6 days. So, in 1 day B does 1/6 amount of work

C takes one more day in addition to the time taken by B. So, C can do the work in 7 days. So, in 1 day C does 1/7 amount of work

When they work together, in 1 day they complete how much work?
In 1 day A, B and C together complete = 1/3 + 1/6 + 1/7 = 9/14 amount of work
A, B and C together complete the entire work in 14/9 days.

১৭.
Working alone, Protik takes complete April to build a pavement. His friend Mahmud is 25% faster than him at the same work. Working alone, how many days will Mahmud take to build the same pavement?
  1. ক
    ক) 20 days
  2. খ
    খ) 24 days
  3. গ
    গ) 22.5 days
  4. ঘ
    ঘ) 37.5 days
ব্যাখ্যা

April has 30 days. So Protik takes 30 days to build the pavement.
Mahmud is 25% faster than Protik

25% = 25/100 = .25
This means, if Protik is 1, then Mahmud is (1 + 0.25) = 1.25
Protik takes 30 days to do the work.
Mahmud will take = 30/1.24 = 24 days to get the work done.

১৮.
Two friends P & Q take a project and start working on it together. P alone can finish the project in 20 days while Q takes 5 days more than P to finish it. After working together on the project for some days, P has to leave. Q now takes 10 days to finish the remaining project alone. After how many days of working together did P leave?
  1. ক
    ক) 5 days
  2. খ
    খ) 6(2/3) days
  3. গ
    গ) 8(1/5) days
  4. ঘ
    ঘ) 10(2/5) days
ব্যাখ্যা

In a days P does 1/20 work; And in 1 day Q does 1/25 work
As seen above, Q works alone for 10 days.
In 1 days Q completes (1/25) × 10 = 2/5 work
Remaining work = 1 - (2/5) = 3/5 = Done by P and Q together
Total Work done = Total days x Work done by all in 1 day

Let P and Q work together for total K days.

∴ 3/5 = K × (1/20 + 1/25)
K = 20/3 = 6(2/3) days = Days when P and Q worked together
Thus P leaves after 6(2/3) days.

১৯.
Working 8 hours a day, A can finish an assignment in 12 days while B takes 2 days less to finish it, working 2 hours more than A, every day. The contractor decides to put them to work together on the assignment. Each working day now is 8 hours. How many days will they take to finish the assignment?
  1. ক
    ক) 60/11 days
  2. খ
    খ) 39/12 days
  3. গ
    গ) 300/49 days
  4. ঘ
    ঘ) 8 days
ব্যাখ্যা

A completes the work in 12 days at 8 hour per day = 12 x 8 = 96 hours
In 1 hour, A completes (1/96) amount of work

B completes the work in 10 days (2 days less than A) working 10 hours every day (i.e. 2 hours more than A per day) = 10 x 10 = 100 hours
In 1 hour, B completes (1/100) amount of work

Working together, in 1 hour A and B complete (1/96) + (1/100) = (49/2400) amount of work
So they complete the entire work in (2400/49) hours

Since they work for 8 hours per day, they need = (2400/49) × (1/8) = 300/49 days.

২০.
Anik and Shuvo are working on a special assignment. Anik needs 6 hours to type 32 pages on a computer and Shuvo needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages?
  1. ক
    ক) 7 hour 30 minutes
  2. খ
    খ) 8 hour 15 minutes
  3. গ
    গ) 7 hour 15 minutes
  4. ঘ
    ঘ) 8 hour 30 minutes
ব্যাখ্যা

Pages typed by Anik in 1 hour = 32/6 = 16/3
Pages typed by Shuvo in 1 hour = 40/5 = 8

Pages typed by Anik and Shuvo in 1 hour = 16/3 + 8 = 40/3
Time taken to type 110 pages when Anik and Shuvo work together = 110 × 3 /40 = 33/4
= 8 (1/4) hours = 8 hour 15 minutes.

২১.
P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if they work together. How much time will Q take to do the work alone?
  1. ক
    ক) 4 days
  2. খ
    খ) 5 days
  3. গ
    গ) 6 days
  4. ঘ
    ঘ) 7 days
ব্যাখ্যা

Let,
The amount of work P does in 1 day = x
Amount of work Q does in 1 day = 2x
Amount of work R does in 1 day = 3x

Amount of work P, Q,R together do in 1 day = x + 2x + 3x = 6x
they can together complete the work in 1 day = (1/6x) days

Given,
1/6x = 2
⇒ 12x = 1
⇒ x = 1/12

Therefore, amount of work Q does in 1 day = 2 × (1/12) = 1/6
That is, Q needs 6 days to complete the work.

২২.
P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in --- days.
  1. ক
    ক) 16 days
  2. খ
    খ) 24 days
  3. গ
    গ) 20 days
  4. ঘ
    ঘ) 12 days
ব্যাখ্যা

Work done by P in 1 day = 1/15
Work done by Q in 1 day = 1/10

Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6
Work done by P and Q in 2 days = 2 × (1/6) = 1/3

Remaining work = 1 - 1/3 = 2/3

Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days

Total time taken = 2 + 10 = 12 days.

২৩.
A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?
  1. ক
    ক) 3(1/5) min
  2. খ
    খ) 3(2/5) min
  3. গ
    গ) 3(3/5) min
  4. ঘ
    ঘ) 3(4/5) min
ব্যাখ্যা

1-minute work done by both the punctures = (1/9) + (1/6)
= (4 + 6)/36
= 10/36
= 5/18

So both punctures will make the type flat in = (18/5) min
= 3(3/5) min

২৪.
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?
  1. ক
    ক) 5 days
  2. খ
    খ) 10 days
  3. গ
    গ) 8 days
  4. 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.

২৫.
Time taken by A to finish a piece of work is twice the time taken B and thrice the time taken by C. If all three of them work together, it takes them 2 days to complete the entire work. How much work was done by B alone?
  1. ক
    ক) 2 days
  2. খ
    খ) 6 days
  3. গ
    গ) 3 days
  4. ঘ
    ঘ) 5 days
ব্যাখ্যা

Time taken by A = x days

Time taken by B = x/2 days

Time Taken by C = x/3 days

⇒ {(1/x) + (2/x) + (3/x) = 1/2

⇒ 6/x = 1/2

⇒ x = 12

Time taken by B = x/2 = 12/2 = 6 days.