1. The document discusses concepts related to time and work, including simultaneous work, alternate day working, and situations where workers start or stop working together. 2. It provides examples of word problems involving time taken by individuals or groups to complete a task and calculates the time taken under various scenarios. 3. The document contains over 30 examples of time and work word problems and their step-by-step solutions. It aims to explain key concepts and build skills for solving such problems.

1. Time and work
Presented by
Assistant Professor Santosh Vishwnath Amande.
MSc (Maths) SET
Trainer of mathematics and reasoning
DGCC, Satara
Lecture 1 – Togethar work or Simultaneous work
And Alternate day working

2. Time and work
1
5
• If ‘A’ can do a work in ‘x’ days then ‘A’s one day work is
1
𝑥
1
5
1
1
5
Sachin complete a work in 5 days then his one day work is
1
5
1
5
1
5
1
5

3. Time and work
• If A’s 1 day work =
1
𝑥
then A can finish the work in ‘x’ days
8
7
6
5
4
3
2
1
Sohan complete a wall in 8 days
after 3 days remaining work

4. Time and work
• Relation between time and work

5. Time and work
A
complete
work in
10 days
B
complete
work in
15 days
If they working together how many days
will they take to complete the work
• Concept of together working and simultaneous working

6. Time and work
• A can complete a work in 20 days and B can do the
same work in 30 days , then time taken to complete
the work
Ans- 12 days

7. Time and work
• A and B working together can finish a piece of work
in 12 days while B alone can finish it in 30 days . In
how many days can A alone finish the work
Ans- 20

8. Time and work
• A completes 1/3 part of the work in 5 days while B complete 2/5
part of the same work in 10 days . In how many days will they
complete doing the work together?
(a) 7
3
4
(b) 9
3
8
(c) 8
4
5
(d) 10 days
1
2
3
Ans- 9
3
days

9. Time and work
• A can do a piece of work in 4 days and B can complete the
same work in 12 days. What is the number of days
required to do the same work together?
(a) 2 (b) 3 (c) 4 (d) 5
Ans- 3 days

10. Time and work
• Ayesha can complete a piece of work in 16 days. Amita can
complete the same piece of work in 8 days. If both of them
work together in how many days can they complete the same
piece of work?
(a) 4 2/5 (b) 5 1/3 days (c) 6 days (d) 12 days (e) None of these
Ans- 5 1/3 days

11. Time and work
• A and B together can complete a particular task in 8 days. If
B alone can complete the same task in 10 days, how many
days will A take to complete the task if he works alone?
• (a) 28 (b) 36 (c) 40 (d) 32 (e) None of these
Ans- 40 days

12. Time and work
• A can finish a work in 18 days and B can do the same
work in half of time taken by A then working together
what part of the same work they can finish in a day
(a) 1/6 (b) 1/9 (c) 2/5 (d) 2/7
Ans- 1/6 days

13. Time and work
Time and work
• A and B together can do a piece of work in 6 days. If A
can alone do the work in 18 days, then the number of days
required for B to finish the work is
(a) 12 (b) 9 (c) 15 (d) 10 (e) None of these
Ans- 9 days

14. • If A and B together can complete a piece of work in 15 days
and B alone in 20 days, in how many days can A alone
complete the work?
(a) 60 (b) 45 (c) 40 (d) 30 (e) None of these
Time and work
Ans- 60 days

15. • A, B and C can do a job working alone in 12, 16 and
24 days respectively. In how many days they can do
the job, if they worked together?
(a) 16/3 (b) 15/4 (c) 17/3 (d) 19/4
Time and work
Ans- 16/3 days

16. Time and work
• A, B and C can complete a work in 2 h. If A does the
job alone in 6 h and B in 5 h, then how long will it
take for C to finish the job alone?
(a) 5 1/2 h (b) 7 ½ h (c) 9 h (d) h 4 1/2
Ans- 7 1/2 days

17. Time and work
• Reena, Aastha and Shloka can independently complete a
piece of work in 6 hours, 4 hours and 12 hours
respectively. If they work together, how much time will
they take to complete that piece of work?
(a) 4 (b) 3 (c) 2 (d) 1 (e) None of these
Ans- 2 days

18. • A, B and C together can do a work in 6 days. A alone can
do it in 12 days while B alone can do it in 18 days, then
time taken by C is
(a) 9 days (b) 18 days (C) 27 days (d) 36 days
Time and work
Ans- 36 days

19. • A, B and C can complete a work in 2 h. If A does the job
alone in 6 h and B in 5 h, then how long will it take for C to
finish the job alone?
(a) 5 1/2 h (b) 7 1/2 h (c) 9 h (d)4 1/2 h
Time and work
Ans- 7 1/2 days

20. Time and work
• Alternate working concept

21. • A and B working separately can do a piece of work in 9 and
15 days, respectively. If they work for a day alternately, with
B beginning, then the work will be completed in
(a) 10 days (b) 11 2/5 days (c) 12 days(d) 13
Time and work
Ans- 11 2/5 days

22. • A and B can complete a piece of work in 12 and 18 days
respectively. A begins to do the work and they work
alternatively one at a time for one day each. The whole
work will be completed in
(a) 14 1/3days (b)15 2/3 days (c) 16 1/3days (d) 18 2/3 days
Time and work
Ans- 14 1/3 days

23. • A, B and C can do a piece of work in 20, 30 and 60 days
respectively. In how many days can A do the work if he is
assisted by B and C on every third day?
(a) 12 days (b) 15 days (c) 16 days (d) 18 days
Time and work
Ans-

24. Time and work
• A can do a work in 20 days and B can do in 10 days. A starts the
work and works alone for 5 days. Then, B joins A and they finish
the work. In how many days the work gets finished?
(a) 10 (b) 12 (c) 9 (d) 8
Ans- 10 days

25. Time and work
• A can do a piece of work in 10 days, while B can do it in 6 days. B
worked at it for 4 days. How long will A take to finish the
remaining work?
(a) 3 1/3days (b) 3 2/3 days (c) 3 2/5 days (d) 3 5/7 days (e) NoT
Ans- 3 1/3 days

26. Time and work
• A and B can do a work in 18 and 24 days, respectively. They
worked together for 8 days and then A left. The remaining work
was finished by B in
(a) 5 days (b) 5 1/3 days (c) 8 days (d) 10 days.
Ans- 5 1/3 days

27. Time and work
• A can complete a piece of work in 18 days, B in 20 days and C
in 30 days. B and C together start the work and are forced. to
leave after 2 days. The time taken by A alone to complete the
remaining work is
(a) 10 days (b) 12 days (c) 15 days (d) 16 days
Ans- 15 days

28. Time and work
• A can do a piece of work in 15 days, which B can do in 10 days. B
worked at it for 8 days. A can finish the remaining work in
(a) 2 days (b) 3 days (c) 5 days (d) 10 days
Ans- 3 days

29. Time and work
• A can do a work in 15 days and B in 20 days. If they work on it
together for 4 days, then the fraction of the work that is left is:
(a) ¼ (b) 1/10 (c) 7/15 (d) 8/15
Ans- 8/15 days

30. Time and work
• A and B can complete a work in 18 days and 15 days respectively.
They started doing the work together but after 3 days A had to
leave and B alone completed the remaining work. The whole
work was completed in
(a) 9 3/4 (b) 10 1/4 (c) 12 ¾ days (d) 12 1/2
Ans- 12 1/2 days

31. Time and work
• A, B and C can separately do a work in 12, 15 and 20 days
respectively. They started to work together but C left after 2 days.
The remaining work will be finished in (R.R.B., 2006)
(a) 4 days (b) 5 days (c) 6 days (d) 15 days
Ans- 4 days

32. Time and work
• A and B can do a piece of work in 30 days, while B and C can do the same
work in 24 days and C and A in 20 days. They all work together for 10 days
when B and C leave. How many days more will A take to finish the work?
(a) 18 days (b) 24 days (c) 30 days (d) 36 days
Ans- 18 days

33. Time and work
• A, B and C together can complete a piece of work in 10 days. All the three
started working at it together and after 4 days A left. Then B and C together
completed the work in 10 more days. A alone could complete the work in:
(a) 15 days (b) 16 days (c) 25 days (d) 50 days
Ans- 25 days

34. Time and work
• A can complete a work in 20 days and B in 30 days. A worked alone for 4
days and then B completed the remaining work along with C in 18 days. In
how many days can C working alone complete the work?
(a) 12 (b) 68 (c) 72 (d) 90
Ans- 90 days

35. Time and work
• A and B can complete a work in 8 days, working together. B alone
can do it in 12 days. After working for 4 days, B left the work.
How many days will A take to complete the remaining work?
(a) 16 (b) 18 (c) 20 (d) 22
Ans- 16 days

36. Time and work
• A mason can build a tank in 12 h. After working for 6 h, he took
the help of a boy and finished the work in another 5 h. The time
that the boy will take alone to complete the work is
(a) 30 h (b) 45 h (c) 60 h (d) 64 h
Ans- 60h

37. • A and B can do a piece of work in 24 and 30 days respectively. Both started
the work and worked for 6 days. Then B leaves the work and C joins and the
remaining work is completed by A and C together in 11 days. Find the days
in which C alone can do the work
(a) 80 (b) 100 (c) 120 (d) 130 (e) None of these
Time and work
Ans- 120 days

38. • A, B and C can alone complete a work in 10, 12 and 15 days
respectively. A and C started the work and after working for 4 days, A
left and B joined. In how many days the total work was completed
(a) 6 5/9 (b) 6 2/9 days (c) 6 days(d) 5 4/9 days (e)NoT
Time and work
Ans- 6 2/9 days

39. • Two persons A and B can do a work in 60 days and 40 days respectively. They
started the work together but A left after some time and B finished the
remaining work in 10 days. After how many days A leave?
• [IBPS RRBS Office Asst. (Pre) 2021]
(a) 12 days (b) 15 days (c) 8 days (d) 18 days (e) None of these
Time and work
Ans- 18 days

40. • A, B and C can complete a work in 12, 20 and 15 days respectively. A and B
started the work and worked for 5 days. Find the time taken by C to complete
the remaining work. [IBPS RRBS Officer Scale-1 (Pre) 2021]
(a) 4 days (b) 5 days (c) 6 days (d) 3 days (e) None of these
Time and work
Ans- 5 days

41. • A can finish a work in 20 days and B can finish the same work in 25 days.
They began together, but B left the work after 5 days. How many more days
will A take to finish the remaining work? [SSC CGL (Pre) 2020]
(a) 11 days (b) 8 days (c) 16 days (d) 21 days
Time and work
Ans- 11 days

42. • A and B can do a work in 12 days, B and C can do the same work
in 15 days, C and A can do the same work in 20 days. The time
taken by A, B and C to do the same work, is
(a) 5 days (b) 10 days (c) 15 days (d) 20 days
Time and work
Ans- 5 days

43. • A and B can do a work in 8 days, B and C can do the same work in
12 days. A, B and C together can finish it in 6 days. A and C
together will do it in
(a) 4 days (b) 6 days (c) 8 days (d) 12 days
Time and work
Ans- 8 days

44. • A and B can do a piece of work in 10 days. B and C can do it in 12
days and C and A in 15 days. In how many days will C finish it
alone?
(a) 24 (b) 30 (c) 40 (d) 60
Time and work
Ans- 40 days

45. • A and B can do a piece of work in 12 days, B and C in 8 days and C
and A in 6 days. How long would B take to do the same work alone?
(a) 24 days (b) 32 days (c) 40 (d) 48 days
Time and work
Ans- 48 days

46. • A and B together can do a work in 12 days. B and C together do it
in 15 days. If A's efficiency is twice that of C, then the days
required for B alone to finish the work, is
(a) 60 (b) 30 (c) 20 (d) 15
Time and work
Ans- 20 days

47. • A and B can do a work in 12 days, B and C in 15 days and C and A in
20 days. If A, B and C work together, they will complete the work in
[RRB (ASM) 2012] (a) 5 days (b) 15 2/3 days (c) 10 days (d) 7 5/6days
Time and work
Ans- 5 days

48. • A and B together can complete a piece of work in 40 days, B and C
can do it in 60 days and C and A can do it in 30 days. A, B and C
together can complete half of the actual work in [SBI PO (Pre) 2021]
(a) 49/3 days (b) 10/3 days(c) 40/3 days (d) 20/3 days (e) 70/3 days
Time and work
Ans- 40/3

49. Time and work
• Efficiency and Time Relation concept

50. • A is thrice as good a workman as B and is, therefore able to
finish a piece of work in 60 days less than B. The time (in days)
in which they can do it working together, is
(a) 22 (b) 23 1/4 (c) 23 (d) 22 1/2
Time and work
Ans-22 1/2

51. • A can complete a piece of work in 12 days. E is 60% more
efficient than A. The number days, that B will take to complete the
same work, is
(a) 6 (b) 7 ½ (c) 8 (d)8 1/2
Ans- 7 1/2
Time and work

52. • Kamal can do a work in 15 days. Bimal is 50% more efficient
than Kamal. The number of days, Bimal will take to do the same
piece of work, is
(a)7 ½ (b) 10 (c) 12 (d) 14
Time and work
Ans- 10 days

53. • A does 20% less work than B. If A can complete a 7 1/2 hours, then
B can piece of work in hours, then B can do it in (S.S.C.2006)
(a) 5 hours (b) 5 1/2hours (c) 6 hours (d) 6 1/2hours
Ans- 6 hours

54. • A is 50% as efficient as B. C does half of the work done by A and
B together. If C alone does the work in 40 days, then A, B and C
together can do the work in:
(a) 13 1/3days (b) 15 days (c) 20 days (d) 30 days
Time and work
Ans- 13 1/3

55. • A is twice as good a workman as B. If they work together, they
can complete a job in 18 days. If A alone does the job, in how
many days he will complete the job?
(a) 27 days (b) 36 days (c) 40 days (d) 54 days
Time and work
Ans- 27 days

56. • A works twice as fast as B. If B can complete a work in 24 days
independently, the number of days in which A and B can together
finish the work is
(a) 12 days (b) 9 days (c) 8 days (d) 6 days (e) None of these
Time and work
Ans- 8 days

57. • X is 3 times as fast as Y and is able to complete the work in 40
days less than Y. Then, thetime in which they can complete the
work together, is
(a) 15 days (b) 10 days (c) 7 1/2 days (d) 5 days
Time and work
Ans- 15 days

58. 𝑀1 × 𝐷1 × 𝑇1 × 𝑊2 = 𝑀2 × 𝐷2 × 𝑇2 × 𝑊1

59. • 20 workers working for 5 h per day complete a work in 10 days. If
25 workers are employed to work 10 h per day, what is the time
required to complete the work?
(a) 4 days (b) 5 days (c) 6 days (d) 8 days
Time and work
Ans- 4 days

60. • 12 men can do a piece of work in 24 days. How many days are
needed to complete the work, if 8 men do this work?
[IDBI PO 2010](a) 28 (b) 36 (c) 48 (d) 52 (e) None of these
Time and work
Ans- 36 days

61. • 15 men complete a work in 16 days. If 24 men are employed, then
the time required to complete that work will be [CDS 2014]
(a) 7 days (b) 8 days (c) 10 days (d) 12 days (e) Not
Time and work
Ans- 10 days

62. • 36 men can do a work in 32 days working 7 h per day, then the
number of men required to complete the same work in 24 days
working 6 h per day, is [SSC (FC) 2012)
(a) 64 (b) 56 (c) 49 (d) 27
Ans- 56
Time and work

63. • 90 men are engaged to do a piece of work in 40 days but it is found
that in 25 days, 2/3 work is completed. How many men should be
allowed to go off, so that the work may be finished in time?
[SSC (10+2) 2008] (a) 10 (b) 15 (c) 20 (d) 25 (e) Not
Time and work
Ans- 15

64. • A contract is to be completed in 92 days and 234 men were set to
work, each working 16 h per day. After 66 days, 4/7 of the work is
completed. How many additional men may be employed, so that the
work may be completed in time, each man now working 18 h per day?
(a) 162 (b) 234 (c) 262 (d) 81 (e) None of these
Time and work
Ans- 162

65. • A contract is to be completed in 50 days and 105 men were set to
work, each working 8 h per day. After 25 days, 2/5 th of the work is
finished. How many additional men be employed, so that the work
may be completed on time, each man now working 9 h per day?
[SNAP 2012] (a) 34 (b)36 (c) 35 (d) 37 (e) NOT.
Time and work
Ans- 35

66. • A contractor undertook to finish a certain work in 124 days and
employed 120 men. After 64 days, he found that he had already
done 2/3 of the work. How many men can be discharged now, so
that the work may finish in time ?
(a) 40 (b) 50 (c) 48 (d) 56 (e) NOT
Time and work
Ans- 56

67. • Seven men can complete a work, in 12 days. They started the
work and after 5 days, two men left. In how many days will the
work be completed by the remaining men?
(a) 5 (b) 6 (c) 7 (d) 8 (e) None of these
Ans- 10

68. Time and work
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