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Free Time and Work MCQs with Answers

120 Time and Work MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

Problems measure work through rates, treating each person's or machine's contribution as work completed per unit time. Questions cover combined work, efficiency, wages, alternate working schedules, pipes and cisterns, and men-days relationships, with care needed to distinguish time taken by one worker from the time required when workers act together.

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120 questions · page 2 of 6

21. P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?

  • A. 5 days
  • B. 10 days
  • C. 15 days
  • D. 12 days

Explanation: P's rate is 1/20 of the work per day and Q's rate is 1/12 of the work per day.

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Correct answer: 10 days

22. P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. how many days does P alone need to finish the remaining work?

  • A. 8
  • B. 6
  • C. 4
  • D. 2

Explanation: Q completes 10 days x 1/15 of the work per day = 2/3 of the work, leaving 1/3.

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Correct answer: 6

23. P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?

  • A. 9(3/5) days
  • B. 9(1/5) days
  • C. 9(2/5) days
  • D. 10 days

Explanation: P, Q and R together work at 1/4 of the track per day, while P and Q together work at 1/16 + 1/12 = 7/48 of the track per day.

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Correct answer: 9(3/5) days

24. wo pipes X and Y fill a tank in 15 hrs. and 20 hrs. respectively, while a third pipe 'Z' can empty the full tank in 25 hrs. All the three pipes are opened in the beginning. After 10 hrs. Z is closed. In how much time, will the tank be full ?

  • A. 12 hrs
  • B. 14 hrs
  • C. 16 hrs
  • D. 18 hrs

Explanation: The combined filling rate of X and Y is 1/15 + 1/20 = 7/60 of the tank per hour, and Z empties 1/25 of the tank per hour, giving an…

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Correct answer: 12 hrs

25. 8 men can dig a pit in 20 days. If a man works half as much again as a boy, then 4 men and 9 boys can dig a similar pit in:__________?

  • A. 12 days
  • B. 16 days
  • C. 18 days
  • D. 20 days

Explanation: If 1 man works 1.5 times as much as 1 boy, then 1 boy equals 2/3 of a man's daily work.

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Correct answer: 16 days

26. Efficiency of Rashid and Danish are in the ratio 5:8. If Danish takes 51 days less than Rashid to complete the work, find the time taken by Rashid to complete the work.

  • A. 85 days
  • B. 126 days
  • C. 118 days
  • D. 136 days

Explanation: Efficiency and time are inversely proportional, so Rashid's and Danish's times are in the ratio 8:5 when their efficiencies are 5:8.

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Correct answer: 136 days

27. If 12 men work 8 hours a day to complete a work in 10 days, how many men working 12 hours a day can complete the work in 5 days?

  • A. 16
  • B. 4
  • C. 12
  • D. 8

Explanation: The total work is 12 men x 8 hours per day x 10 days = 960 man-hours. At 12 hours per day for 5 days, each man supplies 60 hours, so the…

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Correct answer: 16

28. If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.

  • A. 15
  • B. 14
  • C. 16
  • D. 13

Explanation: Forty women working for 30 days provide 40 x 30 = 1,200 woman-days, so a woman's wage is Rs.21,600 ÷ 1,200 woman-days = Rs.18 per day.

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Correct answer: 16

29. Mansoor-Ul-Haque and Aaqib are working on a special assignment. Mansoor-Ul-Haque needs 6 hours to type 32 pages on a computer and Aaqib 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?

  • A. 7 hour 15 minutes
  • B. 7 hour 30 minutes
  • C. 8 hour 15 minutes
  • D. 8 hour 30 minutes

Explanation: Mansoor types 32 pages ÷ 6 hours = 16/3 pages per hour, while Aaqib types 40 pages ÷ 5 hours = 8 pages per hour.

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Correct answer: 8 hour 15 minutes

30. 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 the same in 12 hours. All the machines started printing at 9 A.M. Machine P is stopped at 11 A.M. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?

  • A. 3 pm
  • B. 2 pm
  • C. 1:00 pm
  • D. 11 am

Explanation: In the first 2 hours, the three machines print 2 x (1/8 + 1/10 + 1/12) = 2 x 37/120 = 37/60 of the job.

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Correct answer: 1:00 pm

31. P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?

  • A. 8/15
  • B. 7/15
  • C. 11/15
  • D. 2/11

Explanation: Their combined rate is 1/15 + 1/20 = 7/60 of the work per day. In 4 days they complete 4 x 7/60 = 7/15 of the work, so the fraction left…

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Correct answer: 8/15

32. A and B can together do a piece of work in 15 days. B alone can do it in 20 days. In how many days can A alone do it ?

  • A. 40 days
  • B. 50 days
  • C. 60 days
  • D. 70 days

Explanation: A and B together complete 1/15 of the work per day, while B alone completes 1/20 per day.

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Correct answer: 60 days

33. Farjan and Kashif can complete a task in 30 days. Farjan leaves after 20 days and Kashif alone completes it in another 25 days. How many days does Farjan alone take to complete the entire task?

  • A. 50
  • B. 75
  • C. 60
  • D. 45

Explanation: Together they complete 20 days x 1/30 of the work per day = 2/3, leaving 1/3 for Kashif.

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Correct answer: 50

34. Jameel can complete a task in 15 hours and Nasir can complete the same task in 12 hours. Jameel starts the task at 9:00 am and stops working at 2:00pm. Nasir starts working on the task at 4:00 pm. At what time is the task completed?

  • A. 12:00 pm
  • B. 2:00 am
  • C. 12:00 am
  • D. 10:00 pm

Explanation: Jameel works from 9:00 am to 2:00 pm, which is 5 hours, and completes 5 hours x 1/15 of the work per hour = 1/3 of the work.

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Correct answer: 12:00 am

35. P can do a work in 24 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in_________days.

  • A. 10
  • B. 9
  • C. 11
  • D. 12

Explanation: Q and R together work at 1/9 + 1/12 = 7/36 of the task per day, so in 3 days they complete 3 x 7/36 = 7/12, leaving 5/12.

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Correct answer: 10

36. Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in________days.

  • A. 14
  • B. 16
  • C. 15
  • D. 11

Explanation: Kamal's rate is 1/20 of the work per day. Suresh is 25% more efficient, so his rate is 1.25 x 1/20 = 1/16 work per day, meaning he needs…

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Correct answer: 16

37. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?

  • A. 37 ½ days
  • B. 22 days
  • C. 31 days
  • D. 22 days

Explanation: A completes 80% in 20 days, so A's rate is 0.8/20 = 0.04 = 1/25 work per day.

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Correct answer: 37 ½ days

38. A can do (1/3) of a work in 5 days and B can do (2/5) of the work in 10 days. In how many days both A and B together can do the work ?

  • A. 75/8 days
  • B. 44/6 days
  • C. 48/5 days
  • D. None of these

Explanation: A's rate is (1/3) / 5 = 1/15 work per day, and B's rate is (2/5) / 10 = 1/25 work per day.

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Correct answer: 75/8 days

39. A alone can finish a work in X days. B alone can finish the same work in X+5 days. Together, they take 6 days to complete the work. Find X

  • A. 12
  • B. 8
  • C. 10
  • D. 9

Explanation: The combined rate equation is 1/X + 1/(X+5) = 1/6. Multiplying through gives 6(2X+5) = X(X+5), so X² - 7X - 30 = 0 = (X-10)(X+3), and the…

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Correct answer: 10

40. P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?

  • A. 7
  • B. 8
  • C. 9
  • D. 10

Explanation: The rates of P+Q, Q+R, and P+Q+R are 1/8, 1/12, and 1/6 work per day. Q's rate is 1/8 + 1/12 - 1/6 = 1/24, so P+R's rate is 1/6 - 1/24 =…

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Correct answer: 8
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