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- Online Time and Work Exercise with Correct Answer Key and Solutions
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- Question 1 of 25
##### 1. Question

Ramesh is twice as good a workman as Sunil and finishes a piece of work in 3 hours less than Sunil. In how many hours they together could finish the same piece of work?

##### Hint

Let Sunil finishes the job in x hours.

Then, Ramesh will finish the job in x/2 hours.

We have,

Therefore, Sunil finishes the job in 6 hours and Ramesh in 3 hours.

Work done by both of them in 1 hour

=

They together finish the piece of work in 2 hours.

- Question 2 of 25
##### 2. Question

Suresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 10 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone?

##### Hint

The part of job that Suresh completes in 9 hours

=

Remaining job

=

Remaining job can be done by Ashutosh in

⅖ × 10 = 4 hours

- Question 3 of 25
##### 3. Question

10 men and 15 women finish a work in 6 days. One man alone finishes that work in 100 days. In how many days will a woman finish the work?

##### Hint

15 women’s work of a day

part

∴ for 1 whole part a woman will take

= 15 × 15 = 225 days.

- Question 4 of 25
##### 4. Question

Sunil and Pradeep can complete a work in 5 days and 15 days respectively. They both work for one day and then Sunil leaves. In how many days in the remaining work completed by Pradeep?

##### Hint

Sunil takes 5 days and Pradeep takes 15 days to do the work.

In a day they would complete

i.e., work.

The remaining 11/15th work would be completed by Pradeep in

i.e. 11 days.

- Question 5 of 25
##### 5. Question

Suresh can finish a piece of work by himself in 42 days. Mahesh, who is ⅕ times more efficient as Suresh, requires X days to finish the work by working all by himself. Then what is the value of X?

##### Hint

Suresh, working alone 42 days = 1 unit of work.

Mahesh is 1/5 times more efficient that Suresh.

So Mahesh is 6/5 times as efficient as Suresh.

Hence Mahesh should require 5/6th of the time, the time taken by Suresh.

Therefore time taken by Mahesh = 5/6 × 42 = 35 days.

- Question 6 of 25
##### 6. Question

Ganpat, Yogesh and Bhagwat can do a job in 15, 20 and 30 days respectively. In how many days can the job be finished if they work together?

##### Hint

Ganpat’s day work = 1/15 of the total.

Yogesh’s 1 day work = 1/20 of the total.

Bhagwat’s 1 day work = 1/30 of the total.

They can do of the total work in 1 day.

⇒ Total work can be finished in

=

=

= days.

- Question 7 of 25
##### 7. Question

If 12 men or 15 women or 18 boys can do a piece of work in 15 days of 8 hours each, find how many men assisted by 5 women and 6 boys will finish the same work in 16 days of 9 hours each.

##### Hint

Given 12 men ≡ 15 women ≡ 18 boys

∴ 1 Man ≡ 1.5 boys, 1 woman = 6/5 boys.

Now, 5W + 6B = 12B.

Required answer is calculated as follows :

Total no. of boys required

= 18 × [(15/16) × (8/9)] = 15 boys

The number of boys already present = 12.

Hence, 3 boys more required.

But 3 boys = 2 men.

So, 2 men are required.

- Question 8 of 25
##### 8. Question

If 6 BSF or 10 CRPF companies can demolish a terrorist outfit in Kashmir in 2 days, find how long will 4 BSF and 9 CRPF companies take to do the same?

##### Hint

Given 6 BSF ≡ 10 CRPF

⇒ 4 BSF + 9 CRPF

= 4 + (9 × 6/10) BSF

= BSF

Now work = 6 × 2 BSF days

= BSF days

We have 6 × 2 ≡

⇒ X = 1.27 days

- Question 9 of 25
##### 9. Question

10 horses and 15 cows eat grass of 5 acres in a certain time. How many acres will feed 15 horses and 10 cows for the same time, supposing a horse eats as much as 2 cows?

##### Hint

1 horse = 2 cows, 10 horses = 20 cows.

⇒ 10 horses + 15 cows = 20 + 15 = 35 cows.

15 horses + 10 cows = 40 cows.

Now 35 cows eat 5 acres.

⇒ 40 cows eat 5 × ⁴⁰⁄₃₅ = 5⁵⁄₇ acres.

Here we have converted everything in terms of cows, you can work in terms of horses also.

- Question 10 of 25
##### 10. Question

2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy to the work?

##### Hint

Let 1 man’s 1 days’ work = x and 1 boy’s 1 day’s work = y

Then, 2x + 3y = 1/10 and 3x + 2y = 1/8

Solving, we get :

and

∴ (2 men + 1 boy)’s 1 day’s work

=

So, 2 men and 1 boy together can finish the work in 12½ days.

- Question 11 of 25
##### 11. Question

A, B and C working together completed a job in 10 days. However, C only worked for the first three days when ³⁄₁₀₀ of the job was done. Also, the work done by A in 5 days is equal to the work done by B in 4 days. How many days would be required by the fastest worker to complete the entire work?

##### Hint

A, B and C’s 1 day’s work = 1/10

i.e. …(1)

Also, only C’s 1 day’s work = 3/100

i.e. … (2)

From the given condition,

…. (3)

By comparing the ratio given in equ (1) and (2),

We can say C is the lowest worker.

Also, from equation (1) and (3), B is the fastest worker.

∴ We have,

{from (1), (2), (3)}

Hence, B completes the entire work in 20 days.

- Question 12 of 25
##### 12. Question

If 15 men or 24 women or 36 boys can do a piece of work in 12 days, working 8 hours a day, how many men must be associated with 12 women and 6 boys to do another piece of work 2¼ times as great in 30 days working 6 hours a day?

##### Hint

Using M₁T₁W₂ = M₂T₂W₁, we get

⇒ x + 10 =

⇒ x = 18 – 10 = 8

Hence, 8 men must be associated.

- Question 13 of 25
##### 13. Question

Ten men can finish a piece of work in 10 days, whereas it takes 12 women to finish it in 10 days. If 15 men and 6 women undertake the work, how many days will they take to complete it?

##### Hint

10 men finishes a work in 10 days and 12 women finishes in 10 days.

∴ 10 men and 12 women finishes a work in 10 days

∴ 15 men and 6 women will complete the work in

days

i.e., in 5 days.

- Question 14 of 25
##### 14. Question

Two men undertake to do a piece of work for Rs 600. One alone could do it in 6 days and the other in 8 days. With the assistance of a boy they finish it in 3 days. Boy’s share should be

##### Hint

1st man can do in 3 days = ³⁄₆ part of the work

2nd man can do in 3 days = ³⁄₈ part of the work

Boy can do in 3 days

part of the work

∴ Ratio of their wages

= 4 : 3 : 1

Boy’s share

- Question 15 of 25
##### 15. Question

Two men undertake to do a piece of work for Rs 1,400. First man alone can do this work in 7 days while the second man alone can do this work in 8 days. If they working together complete this work in 3 days with the help of a boy, how should money be divided?

##### Hint

1st man can do in 3 days =³⁄₇ part of the work

2nd man can do in 3 days ³⁄₈ part of the work

Boy can do in 3 days

=

part of the work

∴ Ratio of their wages

= 24 : 21 : 11

∴ 1st man’s share

=

2nd man’s share

Boy’s share

- Question 16 of 25
##### 16. Question

4 men and 10 women were put on a work. They completed ⅓ of the work in 4 days. After this 2 men and 2 women were increased. They completed ²⁄₉ more of the work in 2 days. If the remaining work is to be completed in 3 days, then how many more women must be increased?

##### Hint

Remaining work

4 men + 10 women do 1 work in 12 days.

6 men + 12 women do 1 work in 9 days.

48 men + 120 women = 54 men + 108 women

⇒ 6 men = 12 women

⇒ 1 men = 2 women

∴ In 12 days 1 work requires 9 men

∴ In 1 day 1 work requires 9 × 12 men

∴ In 3 days 1 work requires

men

∴ In 3 days ⁴⁄₉ work requires

men

There are 6 men and 12 women or (12 men equivalent)

So, 4 men equivalent is required additionally

∴ 8 women are needed to finish the work.

- Question 17 of 25
##### 17. Question

A can do 50% more work as B can do in the same time. B alone can do a piece of work in 20 hours. A, with help of B, can finish the same work in how many hours?

##### Hint

In one hr. B finishes ¹⁄₂₀ of the work.

In one hr. A finishes

of the work.

A+B finish

of the work in 1 hr.

Both of them will take 8 hrs. to finish the work.

- Question 18 of 25
##### 18. Question

A man is twice as fast as a woman. Together the man and the woman do the piece of work in 8 days. In how many days each will do the work if engaged alone?

##### Hint

Let the man alone do the work in x days.

then, the woman alone do the work in 2x days.

Their one day’s work = ⅛th part of whole work

i.e.

⇒ x = 12 days

∴ man takes 12 days and woman 2x = 24 days.

- Question 19 of 25
##### 19. Question

X and Y can do job in 25 days and 30 days respectively. They work together for 5 days and then X leaves. Y will finish the rest of the work in how many days?

##### Hint

X’s one day’s work = ¹⁄₂₅th part of whole work.

Y’s one day’s work = ¹⁄₃₀th part of whole work.

Their one day’s work

= part of whole work.

Now, work is done in 5 days

of whole work

∴ Remaining work

= of whole work

Now, ¹⁄₃₀th work is done by y in one day.

∴ ¹⁹⁄₃₀th work is done by y in

- Question 20 of 25
##### 20. Question

A and B can do a job in 16 days and 12 days respectively. 4 days before finishing the job, A joins B. B has started the work alone. Find how many days B has worked alone?

##### Hint

A’s one day’s work = ¹⁄₁₆ th work

B’s one day’s work = ¹⁄₁₂th work

Let B has worked alone = x days. Then,

A’s amount of work + B’s amount of work = 1

⇒ x = 5 days

- Question 21 of 25
##### 21. Question

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

##### Hint

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

A’s 1 day’s work = ¹⁄₂₃th;

B’s 1 days work = ¹⁰⁄₂₉₉

(A + B)’s 1 day’s work

=

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

- Question 22 of 25
##### 22. Question

A man, a woman or a boy can do a job in 20 days, 30 days or 60 days respectively. How many boys must assist 2 men and 8 women to do the work in 2 days?

##### Hint

Man’s two day’s work

= 2×¹⁄₂₀th work

Woman’s two days’s work

Boy’s two day’s work

= 2×¹⁄₆₀th work = ¹⁄₃₀th work

Now, let 2 men, 8 women and x boys can complete work in 2 days. Then ,

2 men’s work +8 women’s work + x boy’s work =1

⇒ x = 8 boys

- Question 23 of 25
##### 23. Question

One hundred men in 10 days do a third of a piece of work. The work is then required to be completed in another 13 days. On the next day (the eleventh day) 50 more men are employed, and on the day after that, another 50. How many men must be discharged at the end of the 18th day so that the rest of the men, working for the remaining time, will just complete the work?

##### Hint

Suppose that X men must be discharged at the end of the 18th day.

100 × 10 + 150 × 1 + 200 × 7 + (200 – X) × 5

= 100 × 30

5X = 550

⇒ X = 110 men

- Question 24 of 25
##### 24. Question

If 15 women or 10 men can complete a project in 55 days, in how many days will 5 women and 4 men working together complete the same project?

##### Hint

15 W = 10 M

Now, 5W + 4M

=

= 5W + 6W = 11 W

If 15 women can complete the project in 55 days,

11 women can complete the same project in

- Question 25 of 25
##### 25. Question

A alone would take 8 days more to complete the job than if both A and B would together. If B worked alone, he took 4½ days more to complete the job than A and B worked together. What time would they take if both A and B worked together?

##### Hint

Let if both A and B work together, they take x days.

∴ (A + B)’s 1 days’s work = 1/xth work.

A’s 1 day’s work

B’s 1 day’s work

Now,

⇒ x(2x + 9 – 2x + 16) = (x + 8)(2x + 9)

⇒ 4x² + 25x = 2x² + 25x + 72

⇒ x² = 36 ⇒ x = 6 days