OU All In One

Time and Work questions

Working together, alone and in shifts.

1. 6 workers can build a wall in 24 days. How many days will 2 workers take to build the same wall?

  1. 72 days
  2. 86 days
  3. 58 days
  4. 54 days
Answer

A. 72 days Work = 6 × 24 = 144 worker-days. 144/2 = 72 days.

2. Nikhil and Fatima together finish a task in 18 days. Nikhil alone takes 30 days. How long will Fatima alone take?

  1. 45 days
  2. 41 days
  3. 54 days
  4. 36 days
Answer

A. 45 days Fatima's rate = 1/18 − 1/30 = 1/45, so 45 days.

3. Divya alone can do a job in 15 days and Rohit alone in 30 days. They work together for 4 days and then Divya leaves. How many more days will Rohit take to finish?

  1. 18 days
  2. 19 days
  3. 23 days
  4. 16 days
Answer

A. 18 days In 4 days they finish 4 × (1/15 + 1/30) = 0.4. Remaining 0.6 at 1/30 per day = 18 days.

4. Divya can finish a job in 12 days and Rohit in 4 days. Working together, in how many days will they finish it?

  1. 1 day
  2. 3 days
  3. 2 days
  4. 4 days
Answer

B. 3 days Work per day = 1/12 + 1/4 = 1/3. Together: 3 days.

5. 4 workers can build a wall in 15 days. How many days will 1 workers take to build the same wall?

  1. 60 days
  2. 58 days
  3. 66 days
  4. 61 days
Answer

A. 60 days Work = 4 × 15 = 60 worker-days. 60/1 = 60 days.

6. Rohit and Ravi together finish a task in 18 days. Rohit alone takes 30 days. How long will Ravi alone take?

  1. 54 days
  2. 43 days
  3. 45 days
  4. 36 days
Answer

C. 45 days Ravi's rate = 1/18 − 1/30 = 1/45, so 45 days.

7. Priya alone can do a job in 20 days and Rahul alone in 30 days. They work together for 3 days and then Priya leaves. How many more days will Rahul take to finish?

  1. 23.5 days
  2. 16.88 days
  3. 27 days
  4. 22.5 days
Answer

D. 22.5 days In 3 days they finish 3 × (1/20 + 1/30) = 0.25. Remaining 0.75 at 1/30 per day = 22.5 days.

8. Rahul can finish a job in 12 days and Meera in 24 days. Working together, in how many days will they finish it?

  1. 8 days
  2. 6 days
  3. 10 days
  4. 9 days
Answer

A. 8 days Work per day = 1/12 + 1/24 = 1/8. Together: 8 days.

9. 5 workers can build a wall in 22 days. How many days will 1 workers take to build the same wall?

  1. 121 days
  2. 110 days
  3. 132 days
  4. 112 days
Answer

B. 110 days Work = 5 × 22 = 110 worker-days. 110/1 = 110 days.

10. Ayesha and Meera together finish a task in 18 days. Ayesha alone takes 30 days. How long will Meera alone take?

  1. 47 days
  2. 54 days
  3. 34 days
  4. 45 days
Answer

D. 45 days Meera's rate = 1/18 − 1/30 = 1/45, so 45 days.

11. Farhan alone can do a job in 15 days and Fatima alone in 30 days. They work together for 2 days and then Farhan leaves. How many more days will Fatima take to finish?

  1. 24 days
  2. 23 days
  3. 25 days
  4. 26 days
Answer

A. 24 days In 2 days they finish 2 × (1/15 + 1/30) = 0.2. Remaining 0.8 at 1/30 per day = 24 days.

12. Rohit can finish a job in 30 days and Zoya in 20 days. Working together, in how many days will they finish it?

  1. 14 days
  2. 9 days
  3. 15 days
  4. 12 days
Answer

D. 12 days Work per day = 1/30 + 1/20 = 1/12. Together: 12 days.

13. 18 workers can build a wall in 21 days. How many days will 6 workers take to build the same wall?

  1. 63 days
  2. 61 days
  3. 57 days
  4. 79 days
Answer

A. 63 days Work = 18 × 21 = 378 worker-days. 378/6 = 63 days.

14. Farhan and Ravi together finish a task in 6 days. Farhan alone takes 10 days. How long will Ravi alone take?

  1. 13 days
  2. 15 days
  3. 19 days
  4. 12 days
Answer

B. 15 days Ravi's rate = 1/6 − 1/10 = 1/15, so 15 days.

15. Meera alone can do a job in 24 days and Farhan alone in 12 days. They work together for 4 days and then Meera leaves. How many more days will Farhan take to finish?

  1. 6 days
  2. 4 days
  3. 8 days
  4. 7 days
Answer

A. 6 days In 4 days they finish 4 × (1/24 + 1/12) = 0.5. Remaining 0.5 at 1/12 per day = 6 days.

16. Ayesha can finish a job in 14 days and Nikhil in 35 days. Working together, in how many days will they finish it?

  1. 13 days
  2. 8 days
  3. 9 days
  4. 10 days
Answer

D. 10 days Work per day = 1/14 + 1/35 = 1/10. Together: 10 days.

17. 8 workers can build a wall in 8 days. How many days will 4 workers take to build the same wall?

  1. 16 days
  2. 14 days
  3. 18 days
  4. 12 days
Answer

A. 16 days Work = 8 × 8 = 64 worker-days. 64/4 = 16 days.

18. Ravi and Zoya together finish a task in 20 days. Ravi alone takes 30 days. How long will Zoya alone take?

  1. 54 days
  2. 60 days
  3. 66 days
  4. 62 days
Answer

B. 60 days Zoya's rate = 1/20 − 1/30 = 1/60, so 60 days.

19. Vikram alone can do a job in 20 days and Meera alone in 30 days. They work together for 4 days and then Vikram leaves. How many more days will Meera take to finish?

  1. 25 days
  2. 20 days
  3. 16 days
  4. 22 days
Answer

B. 20 days In 4 days they finish 4 × (1/20 + 1/30) = 0.33. Remaining 0.67 at 1/30 per day = 20 days.

20. Rohit can finish a job in 8 days and Arjun in 24 days. Working together, in how many days will they finish it?

  1. 8 days
  2. 7 days
  3. 6 days
  4. 4 days
Answer

C. 6 days Work per day = 1/8 + 1/24 = 1/6. Together: 6 days.

21. 10 workers can build a wall in 13 days. How many days will 5 workers take to build the same wall?

  1. 23 days
  2. 26 days
  3. 31 days
  4. 21 days
Answer

B. 26 days Work = 10 × 13 = 130 worker-days. 130/5 = 26 days.

22. Kiran and Rohit together finish a task in 12 days. Kiran alone takes 20 days. How long will Rohit alone take?

  1. 32 days
  2. 23 days
  3. 30 days
  4. 31 days
Answer

C. 30 days Rohit's rate = 1/12 − 1/20 = 1/30, so 30 days.

23. Ravi alone can do a job in 24 days and Fatima alone in 12 days. They work together for 4 days and then Ravi leaves. How many more days will Fatima take to finish?

  1. 5 days
  2. 4 days
  3. 6 days
  4. 8 days
Answer

C. 6 days In 4 days they finish 4 × (1/24 + 1/12) = 0.5. Remaining 0.5 at 1/12 per day = 6 days.

24. Farhan can finish a job in 20 days and Rahul in 30 days. Working together, in how many days will they finish it?

  1. 11 days
  2. 9 days
  3. 12 days
  4. 10 days
Answer

C. 12 days Work per day = 1/20 + 1/30 = 1/12. Together: 12 days.

25. 20 workers can build a wall in 28 days. How many days will 4 workers take to build the same wall?

  1. 126 days
  2. 140 days
  3. 141 days
  4. 154 days
Answer

B. 140 days Work = 20 × 28 = 560 worker-days. 560/4 = 140 days.

26. Ravi and Sana together finish a task in 6 days. Ravi alone takes 10 days. How long will Sana alone take?

  1. 14 days
  2. 18 days
  3. 13 days
  4. 15 days
Answer

D. 15 days Sana's rate = 1/6 − 1/10 = 1/15, so 15 days.

27. Nikhil alone can do a job in 6 days and Imran alone in 12 days. They work together for 3 days and then Nikhil leaves. How many more days will Imran take to finish?

  1. 3 days
  2. 5 days
  3. 1 day
  4. 2 days
Answer

A. 3 days In 3 days they finish 3 × (1/6 + 1/12) = 0.75. Remaining 0.25 at 1/12 per day = 3 days.

28. Farhan can finish a job in 21 days and Sana in 42 days. Working together, in how many days will they finish it?

  1. 12 days
  2. 11 days
  3. 16 days
  4. 14 days
Answer

D. 14 days Work per day = 1/21 + 1/42 = 1/14. Together: 14 days.

29. 9 workers can build a wall in 14 days. How many days will 3 workers take to build the same wall?

  1. 34 days
  2. 42 days
  3. 53 days
  4. 43 days
Answer

B. 42 days Work = 9 × 14 = 126 worker-days. 126/3 = 42 days.

30. Farhan and Sana together finish a task in 8 days. Farhan alone takes 12 days. How long will Sana alone take?

  1. 26 days
  2. 19 days
  3. 24 days
  4. 23 days
Answer

C. 24 days Sana's rate = 1/8 − 1/12 = 1/24, so 24 days.

31. Meera alone can do a job in 10 days and Zoya alone in 15 days. They work together for 2 days and then Meera leaves. How many more days will Zoya take to finish?

  1. 9 days
  2. 11 days
  3. 13 days
  4. 10 days
Answer

D. 10 days In 2 days they finish 2 × (1/10 + 1/15) = 0.33. Remaining 0.67 at 1/15 per day = 10 days.

32. Vikram can finish a job in 18 days and Ravi in 9 days. Working together, in how many days will they finish it?

  1. 7 days
  2. 5 days
  3. 6 days
  4. 8 days
Answer

C. 6 days Work per day = 1/18 + 1/9 = 1/6. Together: 6 days.

33. 20 workers can build a wall in 17 days. How many days will 5 workers take to build the same wall?

  1. 68 days
  2. 51 days
  3. 67 days
  4. 70 days
Answer

A. 68 days Work = 20 × 17 = 340 worker-days. 340/5 = 68 days.

34. Vikram and Zoya together finish a task in 15 days. Vikram alone takes 20 days. How long will Zoya alone take?

  1. 59 days
  2. 45 days
  3. 66 days
  4. 60 days
Answer

D. 60 days Zoya's rate = 1/15 − 1/20 = 1/60, so 60 days.

35. Vikram alone can do a job in 20 days and Priya alone in 30 days. They work together for 3 days and then Vikram leaves. How many more days will Priya take to finish?

  1. 24.75 days
  2. 22.5 days
  3. 24.5 days
  4. 20.5 days
Answer

B. 22.5 days In 3 days they finish 3 × (1/20 + 1/30) = 0.25. Remaining 0.75 at 1/30 per day = 22.5 days.

36. Sana can finish a job in 18 days and Vikram in 9 days. Working together, in how many days will they finish it?

  1. 7 days
  2. 5 days
  3. 8 days
  4. 6 days
Answer

D. 6 days Work per day = 1/18 + 1/9 = 1/6. Together: 6 days.

37. 5 workers can build a wall in 20 days. How many days will 1 workers take to build the same wall?

  1. 125 days
  2. 90 days
  3. 100 days
  4. 120 days
Answer

C. 100 days Work = 5 × 20 = 100 worker-days. 100/1 = 100 days.

38. Imran and Fatima together finish a task in 18 days. Imran alone takes 30 days. How long will Fatima alone take?

  1. 46 days
  2. 45 days
  3. 54 days
  4. 56 days
Answer

B. 45 days Fatima's rate = 1/18 − 1/30 = 1/45, so 45 days.

39. Farhan alone can do a job in 6 days and Vikram alone in 12 days. They work together for 3 days and then Farhan leaves. How many more days will Vikram take to finish?

  1. 1 day
  2. 3 days
  3. 4 days
  4. 2 days
Answer

B. 3 days In 3 days they finish 3 × (1/6 + 1/12) = 0.75. Remaining 0.25 at 1/12 per day = 3 days.

40. Sana can finish a job in 6 days and Arjun in 12 days. Working together, in how many days will they finish it?

  1. 2 days
  2. 6 days
  3. 4 days
  4. 3 days
Answer

C. 4 days Work per day = 1/6 + 1/12 = 1/4. Together: 4 days.

41. Ravi and Rohit together finish a task in 18 days. Ravi alone takes 30 days. How long will Rohit alone take?

  1. 45 days
  2. 46 days
  3. 41 days
  4. 50 days
Answer

A. 45 days Rohit's rate = 1/18 − 1/30 = 1/45, so 45 days.

42. Arjun alone can do a job in 12 days and Sana alone in 18 days. They work together for 2 days and then Arjun leaves. How many more days will Sana take to finish?

  1. 15 days
  2. 13 days
  3. 10 days
  4. 16 days
Answer

B. 13 days In 2 days they finish 2 × (1/12 + 1/18) = 0.28. Remaining 0.72 at 1/18 per day = 13 days.

43. Priya can finish a job in 10 days and Nikhil in 15 days. Working together, in how many days will they finish it?

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

A. 6 days Work per day = 1/10 + 1/15 = 1/6. Together: 6 days.

44. Priya and Rohit together finish a task in 12 days. Priya alone takes 20 days. How long will Rohit alone take?

  1. 30 days
  2. 23 days
  3. 33 days
  4. 38 days
Answer

A. 30 days Rohit's rate = 1/12 − 1/20 = 1/30, so 30 days.

45. Rahul alone can do a job in 6 days and Nikhil alone in 12 days. They work together for 2 days and then Rahul leaves. How many more days will Nikhil take to finish?

  1. 8 days
  2. 4 days
  3. 6 days
  4. 5 days
Answer

C. 6 days In 2 days they finish 2 × (1/6 + 1/12) = 0.5. Remaining 0.5 at 1/12 per day = 6 days.

46. Zoya can finish a job in 40 days and Ayesha in 60 days. Working together, in how many days will they finish it?

  1. 23 days
  2. 26 days
  3. 30 days
  4. 24 days
Answer

D. 24 days Work per day = 1/40 + 1/60 = 1/24. Together: 24 days.

47. Zoya and Meera together finish a task in 8 days. Zoya alone takes 12 days. How long will Meera alone take?

  1. 19 days
  2. 24 days
  3. 25 days
  4. 18 days
Answer

B. 24 days Meera's rate = 1/8 − 1/12 = 1/24, so 24 days.

48. Divya alone can do a job in 24 days and Fatima alone in 12 days. They work together for 3 days and then Divya leaves. How many more days will Fatima take to finish?

  1. 9 days
  2. 6.75 days
  3. 6.5 days
  4. 7.5 days
Answer

D. 7.5 days In 3 days they finish 3 × (1/24 + 1/12) = 0.38. Remaining 0.63 at 1/12 per day = 7.5 days.

49. Fatima and Farhan together finish a task in 8 days. Fatima alone takes 12 days. How long will Farhan alone take?

  1. 18 days
  2. 22 days
  3. 30 days
  4. 24 days
Answer

D. 24 days Farhan's rate = 1/8 − 1/12 = 1/24, so 24 days.

50. Fatima and Meera together finish a task in 20 days. Fatima alone takes 30 days. How long will Meera alone take?

  1. 66 days
  2. 72 days
  3. 60 days
  4. 59 days
Answer

C. 60 days Meera's rate = 1/20 − 1/30 = 1/60, so 60 days.

51. A worker completes 92 units of work in 2 days at a constant rate. How many units will they complete in 8 days?

  1. 367
  2. 368
  3. 370
  4. 361
Answer

B. 368 Daily output = 92/2 = 46; in 8 days = 368.

52. A worker completes 901 units of work in 17 days at a constant rate. How many units will they complete in 5 days?

  1. 270
  2. 265
  3. 263
  4. 268
Answer

B. 265 Daily output = 901/17 = 53; in 5 days = 265.

53. A worker completes 2340 units of work in 20 days at a constant rate. How many units will they complete in 8 days?

  1. 937
  2. 935
  3. 936
  4. 931
Answer

C. 936 Daily output = 2340/20 = 117; in 8 days = 936.

54. A worker completes 560 units of work in 8 days at a constant rate. How many units will they complete in 8 days?

  1. 567
  2. 557
  3. 550
  4. 560
Answer

D. 560 Daily output = 560/8 = 70; in 8 days = 560.

55. A worker completes 1938 units of work in 19 days at a constant rate. How many units will they complete in 6 days?

  1. 609
  2. 613
  3. 612
  4. 615
Answer

C. 612 Daily output = 1938/19 = 102; in 6 days = 612.

56. A worker completes 315 units of work in 15 days at a constant rate. How many units will they complete in 2 days?

  1. 35
  2. 42
  3. 43
  4. 37
Answer

B. 42 Daily output = 315/15 = 21; in 2 days = 42.

57. A worker completes 2147 units of work in 19 days at a constant rate. How many units will they complete in 8 days?

  1. 904
  2. 909
  3. 903
  4. 906
Answer

A. 904 Daily output = 2147/19 = 113; in 8 days = 904.

58. A worker completes 425 units of work in 17 days at a constant rate. How many units will they complete in 2 days?

  1. 55
  2. 50
  3. 52
  4. 60
Answer

B. 50 Daily output = 425/17 = 25; in 2 days = 50.

59. A worker completes 429 units of work in 11 days at a constant rate. How many units will they complete in 10 days?

  1. 383
  2. 387
  3. 390
  4. 385
Answer

C. 390 Daily output = 429/11 = 39; in 10 days = 390.

60. A worker completes 2052 units of work in 18 days at a constant rate. How many units will they complete in 14 days?

  1. 1596
  2. 1586
  3. 1597
  4. 1603
Answer

A. 1596 Daily output = 2052/18 = 114; in 14 days = 1596.

61. A worker completes 585 units of work in 13 days at a constant rate. How many units will they complete in 10 days?

  1. 445
  2. 457
  3. 450
  4. 452
Answer

C. 450 Daily output = 585/13 = 45; in 10 days = 450.

62. A worker completes 231 units of work in 7 days at a constant rate. How many units will they complete in 4 days?

  1. 139
  2. 133
  3. 132
  4. 131
Answer

C. 132 Daily output = 231/7 = 33; in 4 days = 132.

63. 10 workers finish a job in 12 days at equal rates. How many days will 6 workers need?

  1. 20
  2. 22
  3. 120
  4. 70
Answer

A. 20 Total work = 10 × 12 = 120 worker-days; days = 120/6 = 20.

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