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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

16 men can complete a piece of work in 8 days. In how many days can 12 men complete the same piece of work?

##### Hint

16 men can complete 1 work in 8 days.

∴ 1 man can complete 1 work in 8 × 16 days

∴ 12 men can complete the same work in

= days.

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

17 men can complete a piece of work in 12 days. In how many days can 6 men complete the same piece of work?

##### Hint

17 men can complete 1 work in 12 days

∴ 1 man can complete the work in 12 × 17 days

∴ 6 men can complete the work in

= 34 days

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

12 Men can complete one-third of the work in 8 days. In how many days can 16 men complete that work?

##### Hint

112 men can complete the whole work in 8 × 3 = 24 days

∴ Required no. of days

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

Computer A takes 3 minutes to process an input while computer B takes 5 minutes. If computers A, B and C can process an average of 14 inputs in one hour, how many minutes does Computer C alone take to process one input?

##### Hint

Part processed by computer A in 1 minute =⅓

Part processed by computer B in 1 minute =⅕

Part processed by computer C in 1 minute

=

Hence, computer C will process 1 input 6 minutes.

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

21 binders can bind 1400 books in 15 days. How many binders will be required to bind 800 books in 20 days?

##### Hint

Required no. of binders

=

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

Vikas gets Rs 350 for every day that he works. If he earns Rs 9,800 in a month of 31 days, for how many days did he work?

##### Hint

Required no. of days

= = 28 days

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

A man can do a piece of work in 10 days but with the assistance of his son, the work is done in 8 days. In how many days, his son alone can do the same piece of work?

##### Hint

(Man + Son)’s one day’s work = ¹⁄₈

Man’s one day’s work =¹⁄₁₀

⇒ Son’s one day’s work

=

∴ Son can do it in 40 days.

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

A can knit a pair of socks in 3 days. B can knit the same thing in 6 days. If they are knitting together, in how many days will they knit two pairs of socks?

##### Hint

A’s one day’s work

.

B’s one day’s work

(A + B)’s one day’s work

∴ A and B together can complete the work (knit a pair of socks) in 2 days.

∴ They together knit two pair of socks in 4 days.

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

A group of US planes can completely destroy Bughdad in 7 days. However 12 planes develop technical faults. The remaining now can do the job in 10 days. Find the original group strength.

##### Hint

We have W = work to be done = Destruction of the city

= X × 7 plane days, where X = original number of planes.

Also, W = (X – 12) × 10 plane days.

Now the work done is same in the two cases (destruction of same city)

⇒ X × 7 ≡ (X – 12) × 10

⇒ X = 40 planes.

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

12 men take 18 days to complete a job whereas 12 women in 18 days can complete ¾ of the same job. How many days will 10 men and 8 women together take to complete the same job?

##### Hint

12 M × 18 = 12 W × 18 × ⁴⁄₃

∴ W = ¾M

10M + 8W = 10M + 8 × ¾M = 16 M

∴ 16 men can complete the same work in

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

A can do ¾ of a work in 12 days. In how many days can he finish ⅛ of the work?

##### Hint

A can do ¾ of of work in 12 days

∴ A can do ⅛ of the work in

= 2 days

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

##### Hint

A’s 1 day’s work

= ¹⁄₁₈ and B’s 1 day’s work = ¹⁄₉

∴ (A + B)’s 1 day’s work

=

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

Bhavika alone would take 8 hours more to complete the job than when Bhavika and Ritika worked together. If Ritika worked alone, she would take 4½ hours more to complete the job than when Bhavika and Ritika worked together. What time would they take if both Bhavika and Ritika worked together?

##### Hint

Let the time taken by Bhavika and Ritika together be x days.

∴ Time taken by Bhavika alone

= x + 8 days

and time taken by Ritika alone

= days

∴ 1 day’s work is

⇒

⇒

⇒

⇒

⇒ 2x² + 16x = 16x + 72

⇒ 2x² = 72

⇒ x = 6 days

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

If 36 men can dig a trench 200 metres long, 3 meters wide and 2 metres deep in 6 days working 10 hours a day. In how many days, working 8 hours a day will 10 men dig a trench 100 metres long, 4 m wide and 3 m deep?

##### Hint

Let in x days 10 men will dig a trench

100 m long , 4 m wide and 3m deep, working 8 hours a day

Since, 36 men can dig a trench in 6 days in 10 hours a day

∴ 36 × 6 × 10 = 8 × 10 × x

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

A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. while machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished?

##### Hint

(P + Q + R)’s 1 hour’s work

=

Work done by P, Q and R in 2 hours

=

Remaining work

=

(Q + R)’s 1 hour’s work

=

Now, ¹¹⁄₆₀work is done by Q and R in 1 hour.

So, ²³⁄₆₀ work will be done by Q and R in

hours ≈ 2 hours.

So, the work will be finished approximately 2 hours after 11 a.m., i.e., around 1 p.m.

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

10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed?

##### Hint

10 men’s 1 day’s work =¹⁄₁₅;

15 women’s 1 day’s work = ¹⁄₁₂.

(10 men + 15 women)’s 1 day’s work

=

∴ 10 men and 15 women will complete the work in

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

A can do a piece of work in 10 days, while B alone can do it in 15 days. They work together for 5 days and the rest of the work is done by C in 2 days. If they get Rs 450 for the whole work, how should they divide the money?

##### Hint

Work done by A and B in 5 days

=

Work remaining

=

∴ C alone can do the work in 6 × 2 = 12 days

Ratio of their share work

=

Share of wages = Rs 225, Rs 150, Rs 75.

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

Two men A and B working together complete a piece of work which it would have taken them 30 and 40 days respectively to complete if they worked separately. If they received a payment of Rs. 2,100, B’s share is :

##### Hint

If A and B work separately then A completes his work in 30 days and B completes his work in 40 days.

∴ Ratio of the days = 30: 40 = 3: 4

⇒ Ratio of the work of A and B = 4 : 3

∴ A´s share = ⁴⁄₇ and B’s share = ³⁄₇

Now, They received Rs. 2100( together).

∴ B will receive a payment of

Rs

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

A contractor undertook to do a piece of work in 9 days. He employed certain number of laboures but 6 of them were absent from the very first day and the rest could finish the work in only 15 days. Find the number of men originally employed.

##### Hint

Let the number of men originally employed be x.

9x = 15(x – 6)

⇒ x = 15

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

X can do a piece of work in 15 days. If he is joined by Y who is 50% more efficient, in what time will X and Y together finish the work?

##### Hint

X’s one day’s work

.

Y’s one day’s work

∴ (x + y)’s one day’s work

Hence, they together finish the work in 6 days.

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

A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of wall?

##### Hint

A’s one day’s work = ⅛th work

B’s one day’s work = ⅓rd work

∴ A’s 4 day’s work = 4 × ⅛ = ½ work

∴ In next two days, total wall

Remaining wall

Now, ⅛th wall is built up by A in one day.

∴ ¹¹⁄₁₂th wall is built up by A in

=

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

12 men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work?

##### Hint

1 man’s 1 day’s work

=

12 men’s 6 day’s work

=

Remaining work

=

18 men’s 1 day’s work

=

⅙ work is done by them in 1 day.

∴ ⅓ work is done by them in 6 × ⅓ = 2 days

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

A can do a piece of work in 9 days and B in 18 days. They begin together, but A goes away 3 days before the work in finished. The work lasts for

##### Hint

Let work will be completed in x days.

Then, work done by A in (x – 3) days + work done by B in x days = 1

⇒ 3x = 24

⇒ x = 8 days.

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

Three men, four women and six children can complete a work in seven 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?

##### Hint

Let 1 woman’s 1 day’s work = x.

Then, 1 man’s 1 day’s work = x/2

and 1 child’s 1 day’s work = x/4

So,

∴ 1 woman alone can complete the work in 49 days.

So, to complete the work in 7 days, women required

=

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

12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, If it is to be completed in 3 days?

##### Hint

1 man’s 1 day’s work = ¹⁄₄₈

1 woman’s 1 day’s work = ¹⁄₆₀

6 men’s 2 day’s work

=

Remaining work

=

Now, ¹⁄₆₀ work is done in 1 day by 1 woman.

So, ¾ work will be done in 3 days by

= 15 women.