Time and Work Practice Test Questions - Quantitative Aptitude -- Free Practice

Question 1

Ramesh can complete a work in 12 days, working 7 hours a day. Suresh can complete the same work in 8 days, working 9 hours a day. If Ramesh and Suresh work together working 7 hours a day, in how many days can they complete the work?

A

7323✓✗

B

5713✓✗

C

6513✓✗

D

6611✓✗

Explanation

Ramesh's total work = 12 × 7 = 84 hours, so his rate = 184 per hour. Suresh's total work = 8 × 9 = 72 hours, so his rate = 172 per hour.
Together = 184 + 172 = 13504 per hour, so they need 50413 hours.
At 7 hours a day, the days = 50413 ÷ 7 = 7213 = 5713 days.

Question 2

A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed?

A

10.25 days✓✗

B

11.5 days✓✗

C

12.75 days✓✗

D

9 days✓✗

Explanation

A completes 19 and B completes 112 of the work per day. In two days (A then B) they complete 19 + 112 = 736.
In 10 days (5 such cycles) they complete 3536. The remaining 136 is done by A on the 11th day in 136 ÷ 19 = 14 day.
Total time = 10 + 0.25 = 10.25 days.

Question 3

What will be share of Rajesh, if together Ramesh and Suresh complete only 711 of the task, and all three had been given the contract to finish the task for Rs. 1100?

A

Rs. 350(411)✓✗

B

Rs. 200✓✗

C

Rs. 400✓✗

D

Rs. 650✓✗

Explanation

Ramesh and Suresh complete 711 of the task, so Rajesh completes 411.
Rajesh's share = 411 × 1100 = Rs. 400.

Question 4

P and Q work together and get a payment of Rs. 1400. P can complete the work alone in just 30 days. But Q takes 40 days to complete the work alone. What is P’s share out of the wages they get?

A

Rs. 800✓✗

B

Rs. 600✓✗

C

Rs. 1000✓✗

D

Rs. 700✓✗

Explanation

P and Q's daily work = 130 and 140, so the ratio of their work = 4 : 3.
P's share = 47 × 1400 = Rs. 800.

Question 5

A can complete a work in 12 days and B can complete in 8 days. A works for 8 hours every day while B works for 10 hours every day. If A and B together start working 8 hours per day, in how many days will they complete the work?

A

8 days✓✗

B

6011 days✓✗

C

3912 days✓✗

D

158 days✓✗

Explanation

A takes 12 × 8 = 96 hours and B takes 8 × 10 = 80 hours to finish the work.
Their combined work per hour = 196 + 180 = 5 + 6480 = 11480.
Total time = 48011 hours. At 8 hours per day, the time = 48011 × 8 = 6011 days.

Question 6

P can do a job in 15 days. In how many days can P and Q together complete the job if Q is twice as fast as P?

A

3 days✓✗

B

5 days✓✗

C

2 days✓✗

D

6 days✓✗

Explanation

P does the job in 15 days. Q is twice as fast as P, so Q takes 7.5 days.
Together: 115 + 215 = 315 = 15 per day, so they take 5 days.

Question 7

A can do 14^th part of work in 10 days and B can do 40% work in 40 days and C can do 13^rd of the work in 13 days. Who will complete the work first?

A

A✓✗

B

B✓✗

C

C✓✗

D

A and C both✓✗

Explanation

A does 14 of the work in 10 days, so A takes 40 days.
B does 40% of the work in 40 days, so B takes 100 days.
C does 13 of the work in 13 days, so C takes 39 days.
C takes the least time, so C finishes the work first.

Question 8

A and B can finish a piece of work in 30 days, B and C can finish it in 15 days, C and A in 10 days. Time taken by them together to do this work is?

A

5 days✓✗

B

2(12) days✓✗

C

7(12) days✓✗

D

10 days✓✗

Explanation

2(A + B + C)'s one-day work = 130 + 115 + 110 = 630 = 15.
A + B + C's one-day work = 110.
They finish the work together in 10 days.

Question 9

Wages of 44 women for 56 days comes to Rs.29568. How many men are needed for 47days to receive Rs. 16920, if the daily wages of a man being 5 times those of a woman?

A

9 men✓✗

B

8 men✓✗

C

6 men✓✗

D

5 men✓✗

Explanation

The wage of 1 woman per day = 2956844 × 56 = Rs. 12, so 1 man earns 5 × 12 = Rs. 60 per day.
Men needed to earn Rs. 16,920 in 47 days = 1692060 × 47 = 6.

Question 10

Total wages of 6 men, 4 women and 8 boys is Rs. 26. If the wages of 6 men is equal to that of 8 women and the wages of 4 women is equal to that of 6 boys, then find out the total wages of 8 men, 6 women and 4 boys?

A

Rs. 32✓✗

B

Rs. 24✓✗

C

Rs. 25✓✗

D

Rs. 29✓✗

Explanation

6 men = 8 women, so 1 man = 43 women. 4 women = 6 boys, so 1 boy = 23 woman.
6 men + 4 women + 8 boys = 8 + 4 + 163 = 523 women = Rs. 26, so 1 woman earns Rs. 1.5.
Then 1 man = Rs. 2 and 1 boy = Rs. 1.
8 men + 6 women + 4 boys = 16 + 9 + 4 = Rs. 29.

Question 11

P and Q together can do a work in 18 days. P alone can do the same work in 27 days. In how many days can Q alone do the same work?

A

54 days✓✗

B

36 days✓✗

C

45 days✓✗

D

9 days✓✗

Explanation

P and Q together do 118 per day and P alone does 127.
Q's one day's work = 118 - 127 = 3 - 254 = 154.
Q alone takes 54 days.

Question 12

When P alone does a work, he takes 25 days more than the time taken by P and Q working together to complete the work. But Q alone takes 9 days more than the time taken by P and Q working together to complete the work. In what time, P and Q together finish this work?

A

18 days✓✗

B

20 days✓✗

C

25 days✓✗

D

15 days✓✗

Explanation

Let P and Q take T days together. P alone takes T + 25 and Q alone takes T + 9.
1T + 25 + 1T + 9 = 1T, which gives T² = 25 × 9 = 225.
T = 15 days.

Question 13

A man and a boy received Rs. 1800 as wages for 3 days for a job they did together. The man's efficiency in the work was 5 times that of the boy. What is the daily wages of the boy?

A

Rs. 100✓✗

B

Rs. 500✓✗

C

Rs. 300✓✗

D

Rs. 900✓✗

Explanation

The wages per day for both = 18003 = Rs. 600.
The man's efficiency is 5 times the boy's, so the wages are shared 5 : 1.
The boy's daily wage = 16 × 600 = Rs. 100.

Question 14

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?

A

6 days✓✗

B

4 days✓✗

C

2 days✓✗

D

3 days✓✗

Explanation

35 men make 70 toys in 8 days of 8 hours, so the work for 70 toys = 35 × 8 × 8 = 2240 man-hours.
For 84 toys the work = 8470 × 2240 = 2688 man-hours.
56 men working 12 hours a day do 56 × 12 = 672 man-hours per day.
Days needed = 2688672 = 4 days.

Question 15

Meena can do a piece of work in 20 days. Kumar can do it in 30 days. They start working together on the work but 10 days before the completion of the work, Kumar leaves. In how many days does the total work get completed?

A

20 days✓✗

B

12 days✓✗

C

6 days✓✗

D

16 days✓✗

Explanation

Let the work be completed in t days. Meena works for all t days and Kumar works for t - 10 days.
t20 + t - 1030 = 1, so 3t + 2(t - 10) = 60 and 5t = 80.
t = 16 days.

Question 16

If 3 men can do a work in 2 days and 4 boys can do the same work in 6 days, then in how many days will the same work be completed by 8 men and 8 boys?

A

2 days✓✗

B

35 Days✓✗

C

1.5 Days✓✗

D

34 Days✓✗

Explanation

3 men complete the work in 2 days, so the work = 6 man-days, and 1 man does 16 per day.
4 boys complete it in 6 days, so the work = 24 boy-days, and 1 boy does 124 per day.
8 men + 8 boys do 86 + 824 = 43 + 13 = 53 per day.
They complete the work in 35 days.

Question 17

P, Q and R take a job for Rs. 640. P and Q together finish 2/5thof the work and rest is done by R alone. What is the share of R?

A

Rs. 256✓✗

B

Rs. 420✓✗

C

Rs. 340✓✗

D

Rs. 384✓✗

Explanation

P and Q together do 25 of the work, so R does the remaining 35.
R's share = 35 × 640 = Rs. 384.

Question 18

Ramesh can do a work in 15 days. Vijay and Ramesh together do the same work in 10days. They received Rs. 1155 for that work. What is share of Ramesh and Vijay?

A

Ramesh = Rs. 770; Vijay = Rs. 385✓✗

B

Ramesh = Rs. 605; Vijay = Rs. 550✓✗

C

Ramesh = Rs. 550; Vijay = Rs. 605✓✗

D

Ramesh = Rs. 385; Vijay = Rs. 770✓✗

Explanation

Ramesh's one day's work = 115 and Ramesh + Vijay's = 110.
Vijay's one day's work = 110 - 115 = 130.
The wages are shared in the ratio of the work: Ramesh : Vijay = 115 : 130 = 2 : 1.
Ramesh gets 23 × 1155 = Rs. 770 and Vijay gets Rs. 385.

Question 19

A man can do a piece of work in 4 days, but with the help of his daughter, he can do it in 3 days. In what time can his daughter do it alone?

A

6 ½ days✓✗

B

7 days✓✗

C

9 ½ days✓✗

D

12 days✓✗

Explanation

The man does 14 and both together do 13 of the work per day.
The daughter's one day's work = 13 - 14 = 112.
The daughter alone takes 12 days.

Question 20

12 men and 18 boys working 7.5 minutes an hour complete a particular piece of work in 60 hours. If a boy’s work is half as efficient as a man’s work, how many boys will be needed to help 21 men to achieve twice the work in 50 hours working 9 minutes in an hour.

A

42✓✗

B

46✓✗

C

48✓✗

D

38✓✗

Explanation

A boy is half as efficient as a man, so 18 boys = 9 men. The first group has 12 + 9 = 21 man-equivalents, working 7.5 minutes an hour for 60 hours: 21 × 7.5 × 60 = 9450 units of work.
Twice the work = 18,900 units in 50 hours at 9 minutes an hour: each man does 9 × 50 = 450 units, so the man-equivalents needed = 18900450 = 42.
21 men are given, so the other 21 man-equivalents are boys: 21 × 2 = 42 boys.

Question 21

58th of a job is completed in 10 days. If a person works at the same pace, how many more days will he take to finish the job?

A

4✓✗

B

5✓✗

C

6✓✗

D

7✓✗

Explanation

58 of the job takes 10 days, so the whole job takes 10 × 85 = 16 days.
The remaining 38 of the job takes 16 - 10 = 6 days.

Question 22

A, B & C can each do a piece of work in 6, 9 & 12 minutes. A completes 12 the job & B completes ⅓. How long will C now take to complete the job?

A

3 min.✓✗

B

1 min.✓✗

C

2 min.✓✗

D

112 min.✓✗

Explanation

A completes 12 and B completes 13, so the remaining work = 1 - 12 - 13 = 16.
C alone does the whole job in 12 minutes, so C takes 16 × 12 = 2 minutes.

Question 23

X & Y can each build a wall in 16 & 32 days. X starts working & Y joins 4 days later. In what time was the wall built?

A

18 days✓✗

B

12 days✓✗

C

14 days✓✗

D

21 days✓✗

Explanation

Let the wall be built in t days. X works t days and Y works t - 4 days.
t16 + t - 432 = 1, so 2t + t - 4 = 32 and t = 12 days.

Question 24

A & B can each do a piece of work in 16 & 24 days. They start together, but A quits 4 days before the job is done. In what time is the job completed?

A

12 days✓✗

B

10 days✓✗

C

1212 days✓✗

D

None of these✓✗

Explanation

Let the job last t days. B works all t days and A works t - 4 days.
t - 416 + t24 = 1, so 3(t - 4) + 2t = 48, that is 5t = 60 and t = 12 days.

Question 25

A & B can each do a piece of work in 15 & 18 days. If A works for 10 days, then how long will B alone take to complete the job?

A

8 days✓✗

B

12 days✓✗

C

5 days✓✗

D

6 days✓✗

Explanation

A does 115 of the work per day, so in 10 days A does 1015 = 23 of the work.
The remaining work = 13. B does 118 per day, so B takes 13 × 18 = 6 days.