# Math Questions for Competitive Exams – Time and Work

## Math Questions on Time and Work

### 01. A and B can do a piece of work in 8 days, B and C can do the same work in 12 days. If A, B, and C can complete the same work in 6 days, in how many days can A and C complete the same work?

1. 8
2. 10
3. 12
4. 16

(A + B)’s 1 day work = 1/8…. (1)

(B + C)’s 1 day work = 1/12…. (2)

(A + B + C)’s 1 day work = 1/6…. (3)

A’s one day work = (3) – (2)

= 1/6 – 1/12 = 1/12

C’s one day work = (3) – (1)

= 1/6 – 1/8 = 1/24

⇒ (A + C)’s 1 day work = 1/12 + 1/24 = 1/8

Therefore (A + C) can do the work in 8 days.

### 02. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, what is the time taken by 15 men and 20 boys in doing the same type of work?

1. 4 days
2. 5 days
3. 6 days
4. 7 days

6 men + 8 boys take 10 days

26 men + 48 boys take 2 days

⇒ 10 x (6m + 8b) = 2 x (26m + 48b)

⇒ 60m + 80b = 52m + 96b

⇒ 8m = 16b or 1m = 2b

Now 6m + 8b = 6m + 4m = 10m

15m + 20b = 15m + 10m = 25m

Thus, if 10 men can do a job in 10 days

then 25 men will do the same work in (10 x 10)/25 days i.e. 4 days.

### 03. 1/48 of a work is completed in half a day by 5 persons. Then, 1/40 of the work, can be completed by 6 persons in how many days?

1. 1
2. 2
3. 3
4. 1/2

5 persons can do 1/48 of the work in 1/2 day

∴ 5 persons can do 1/24 of work in one day

⇒ 1 person can do 1/5 of 24 i.e., 1/120 of the work in one day

∴ 6 persons can do 6 x 1/120 or 1/20 of the work in 1

Hence to do 1/40 of the work 1/2 day would be sufficient

### 04.  ‘X’ completes a job in 2 days and ‘Y’ completes it in 3 days and ‘Z’ takes 4 days to complete it. If they work together and get Rs. 3,900 for the day, then how much amount does ‘Y’ get?

1. Rs. 1,800
2. Rs. 1,200
3. Rs. 900
4. Rs. 800

Work done by X, Y, Z together in 1 day = 1/2 + 1/3 + 1/4 = 13/12 of work

Therefore, the whole work is done in 12/13 of a day

Daily wages of Y = 1/3 x Rs. 3,900 = Rs. 1,300

Therefore amount Y gets = 12/13 x Rs. 1,300 = Rs. 1,200

### 05. 76 ladies complete a job in 33 days. Due to some reason some ladies did not join the work and therefore it was completed in 44 days. The number of ladies who did not report for the work is

1. 17
2. 18
3. 19
4. 20

Work requires 76 x 33 = 2508 man days

If N ladies did not report for work

Then (76 – N) x 44 = 2508

76 – N = 2508/44 = 57

N = 76 – 57 = 19

### 06. If one man or two women or three boys can do a piece of work in 55 days, then one man, one woman and one boy will do it in how many days?

1. 20 days
2. 30 days
3. 40 days
4. 50 days

1 man = 3 boys = 2 women

Therefore 1 man + 1 woman + 1 boy = 3 boys + 3/2 boys + 1 boy = 11/ 2 boys.

Now, 3 boys take 55 days

So 11/2 boys take (3 x 55)/11/2 days

= 30 days.

### 07. ‘A’ can do a piece of work in ‘x’ days and ‘B’ can do the same work in 3x days. To finish the work together they take 12 days. What is ‘x’ equal to?

1. 8
2. 10
3. 12
4. 16

1/x + 1/3x = 1/12

(3 + 1)/3x = 1/12

or 4/3x = 1/12

or 3x/4 = 12

or x = (4 x 12)/3 = 16

### 08. A and B can do a piece of work in 10 hours. B and C can do it in 15 hours, while A and C take 12 hours to complete the work. B independently can complete the work in:

1. 12 hours
2. 16 hours
3. 20 hours
4. 24 hours

1/A + 1/B = 1/10

1/B + 1/C = 1/15

1/A + 1/C = 1/12

2(1/A + 1/B + 1/C) = 1/10 + 1/15 + 1/12

⇒ 2(1/A + 1/B + 1/C) = (6 + 4 + 5)/60

⇒ 2(1/A + 1/B + 1/C) = 15/60 = 1/4

⇒ 1/A + 1/B + 1/C = 1/8

⇒ (1/A + 1/C) + 1/B = 1/8

⇒ 1/B = 1/8 – 1/12 = (3 – 2)/24 = 1/24

B takes 24 hours

### 09. 45 people take 18 days to dig a pond. If the pond would have to be dug in 15 days, then the number of people to be employed will be:

1. 50
2. 54
3. 60
4. 72

A case of inverse proportion in which more people would take less day Number of people required = (45 x 18)/15 = 54 people

### 10. X can do a piece of work in 25 days. Y is 25% more efficient than X. The number of days taken by Y is:

1. 15 days
2. 20 days
3. 21 days
4. 30 days

Similar to Q. 14

⇒ D = (25 x 100)/125 = 10

Time of Y = 2500/ 125 = 20 days

### 11. X and Y can do a work in 12 days. Y and Z in 15 days. Z and X in 20 days. If A, B and C work together, they will complete the work in:

1. 5 days
2. 56 days
3. 10 days
4. 15 23 days

X and Y can do 1⁄12th of work in 1 day

Y and Z can do 1⁄15th of work in 1 day

Z and X can do 1⁄20th of work in 1 day

= > (X + Y) + (Y +Z) + (Z + X) = 1⁄12 + 1⁄15 + 1⁄20

= > 2(X +Y +Z) = (5 + 4 + 3)/60

= > X + Y + Z = 1/10

Therefore working together X, Y and Z can complete the work in 10 days.

### 12. A is thrice as good workman as B and therefore, able to finish a job in 60 days less than B. Working together they will do it in?

1. 20 days
2. 30 days
3. 25 days
4. 22½ days

From the question, if A can do the work in x days, B can do the work in 3x days.

Difference of 2x days ( 3x – x) is equal to 60 days ——- (given)

Thus x = 30 days i.e. time taken by A is 30 and by B is 90 days.

A can do 1/30 of the work in 1 day and B can do 1/90 of work in 1 day.

⇒ A and B can both do 1/30 and 1/90 of the work in 1 day

⇒ 1/30 + 1/90 = 2/45 of work in 1 day

Time taken by A and B to complete the whole work = 45/2 days.

Working together they completed the work in 22½ days.

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

1. 7 hrs 30 mts
2. 8 hrs
3. 8 hrs 15 mts
4. 8 hrs 25 mts

Ronald can type 32 pages in 6 hours or 32/6 pages in 1 hour

Elan can type 40 pages in 5 hours or 40/5 = 8 pages in 1 hour

Together they can type 8 + 32/6 pages or 80/6 pages in 1 hour

To type 110 pages they would require 110 ÷ 80/6 hours

660/80 = 33/4 = 8 hrs 15 minutes.

### 14. If 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys to do the same type of work will be

1. 4 days
2. 5 days
3. 6 days
4. 7 days.

Work done by 6 men & 8 boys in 10 days is equal to work done by 26 men & 47 boys in 2 days

Therefore (6 men + 8 boys) x 10 = (26 men + 48 boys) x 2 days

Solving the above equation we get, 8 men = 16 boys or 1 man = 2 boys

Applying the above

26 men + 48 boys = 26 men + 24 men = 50 men

And, 15 men + 20 boys = 15 men + 10 men = 25 men

Therefore, if 50 men can do a work in 2 days, 25 men will do it in 4 days

15 men and 20 boys can do the work in 4 days.

### 15. A and B can do a work in 18 and 24 days respectively. They worked together for 8 days and then A left. The remaining work was finished by B in:

1. 1/3 days
2. 5 days
3. 8 days
4. 10 days.

A’s one days work = 1/18, B’s one day’s work = 1/24.

Working together they can finish:

(1/18) + (1/24) = 7/72th of work in 1 day.

However, they worked only for 8 days together

= (7/72) x 8 = 7/9th of work was finished by A and B together

Remaining work = 1 – 7/9 = 2/9.

Time taken to finish the remaining 2/9 work by B

= (2/9) work x 24 days (since B finishes 1/24 of work in 1 day)

= 16/3 days or 5 1/3 days.

Remaining work was done by B in 5(1/3) days.

### 16.  A can do a certain work in the same time in which B and C together can do it. If A and B could together do it in 10 days and C alone in 50 days, then B alone could do it in

1. 15 days
2. 20 days
3. 25 days
4. 30 days

A & B can do 1/10 of the work in 1 day while C can do 1/50 work in 1 day.

Working together A, B and C can do 1/10 + 1/50 work or 3/25 work in 1 day

But work by A alone is equal to work by B and C together —— (given)

Thus 3/25 of the work done by A + B + C is work done by A + A.

⇒ A alone can do ½ x (3/25) = 3/50 of the work in 1 day

But A and B can do 1/10 of the work in 1 day

∴ B alone can do 1/10 – 3/50 = 1/25 of the work in 1 day

i.e. B can do the work in 25 days

### 17. A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?

1. 1
2. 4
3. 19
4. 41

We need to find the following:

(1) work done by 1 man + 1 woman in 1/4th of a day and

(2) how many boys can do the remaining work in 1/4th of a day

1 day’s work of a man = 1/3, a woman = 1/4, a boy = 1/12

Work done by 1 man + 1 woman in 1/4th of a day = [1/3 + 1/4] x 1/4 = 7/48

Remaining work = 1 – 7/48 = 41/48 —— (i)

A boy’s 1/4 day’s work = 1/4 x 1/12 = 1/48 —— (ii)

From (i) and (ii) it is clear that 41 boys would be required to complete 41/48 work in 1/4 th of a day

### 18. A contractor undertakes to make a road in 40 days and employs 25 men. After 24 days he finds that only one-third of the road is made. How many extra men should he employ so that he is able to complete the work 4 days earlier?

1. 100
2. 60
3. 75
4. 25

25 men can do 1/3 work in 24 days

25 men can do the whole work in 24 x 3 = 72 days

1 man can do the whole work in 72 x 25 = 1800 days

Remaining work is 1 – (1/3) = 2/3

1 man can do the 2/3 of the work in = 2/3 x 1800 = 1200 days

Days left = 36 – 24 = 12 days (since the work is expected to be completed 4 days earlier.

Men required to complete the work in 12 days = 1200/12 = 100 men

Extra men to be employed = 100 – 25 = 75

### 19. A, B and C can do a piece of work individually in 8, 12 and 15 days respectively. A and B start working, but A quits after working for 2 days. After this, C joins B till the completion of work. In how many days will the work be completed?

1. 8/9 days
2. 6/6 days
3. 7/13 days
4. 3/3 days

If the total number of days be n, then B and C work for (n – 2) days.

∴ 2 x (1/8 + 1/12) + (n – 2)(1/12 + 1/15) = 1

⇒ 2 x 5/24 + (n – 2) x 9/60 = 1

⇒ 5/12 + (n – 2) x 3/20 = 1

⇒ (n – 2) x 3/20 = 1 – 5/12 = 7/12

⇒ n – 2 = (7/12) x (20/3) = 35/9 ⇒ n = 2 + 35/9 = 53/9 = 5 8/9

1. 7 days
2. 8 days
3. 10 days
4. 12 days