Time and Work problems
- 1. A and B can complete a work in 12 days and 18 days, respectively. A begins to do the work and they work alternately one at a time for 1 days each. The whole work will be completed in how many days?
Options- A. 142/3
- B. 141/3
- C. 143/5
- D. 145/7 Discuss
Correct Answer: 141/3
Explanation:
(A + B)'s 2 day's work = (1/12) + (1/18) = 5/36
(A + B)'s 14 day's work = (5/36) x 7 = 35/36
Remaining work = 1 - (35/36) = 1/36
Now, it is the turn of A .
A's 1 day's work = 1/12
? 1/36 work is done by A in 12 x (1/36) days = 1/3 days
? Total time taken = 141/3 days
- 2. A can build up a structure in 8 days and 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 structure?
Options- A. 10 days
- B. 9 days
- C. 12 days
- D. 13 days Discuss
Correct Answer:
Explanation:
A,s 1 days work =1/8
B's 1 day's work in breaking the building = 1/3
Now, according to the question,
A's 4 day's work = 4 x (1/8) = 1/2
Now, A's and B's 2 day's work
= 2[(1/8) - (1/3)] = 2 x (-5/24) = -10/24
Total work done in 6 days = 1/2 + (-10/24) = (12 - 10)/24 = 2/24 = 1/12
Remaining work = 1 - (1/12) = 11/12
Now, A has complete the work, so A can complete in N days.
(1/8) x N = 11/12
? N = (11 x 8) / 12
N = (11 x 2)/3 = 71/3 days
- 3. Mr. Prashant has to build a wall 1000 meters long in 50 days. He employs 56 men but at the end of 27 days finds that only 448 meters are built. How many men must be employed so that the work may be finished in time?
Options- A. 81
- B. 38
- C. 25
- D. 58 Discuss
Correct Answer: 25
Explanation:
Y = 56 x (27/23) x (552/448)
=81
Extra men required =81-56
=25
- 4. Mr. Modi can copy 40 pages in 10 minutes, Mr. Xerox and Mr. Modi both working together can copy 250 In 25 minutes. In how many minutes Mr. Xerox can copy 36 pages?
Options- A. 5 minutes
- B. 6 minutes
- C. 3 minutes
- D. 12 minutes Discuss
Correct Answer: 6 minutes
Explanation:
Efficiency ( per minute) of Modi = 4 copies/min
Efficiency of Modi and Xerox together = 10 pages/min
? Efficiency of Xerox alone = 10 - 4 = 6 pages/min
? Mr. Xerox needs 6 min to copy 36 pages.
- 5. 25 men and 15 women can complete a piece of work in 12 days. All of them start working together and after working for 8 days the women stopped working. 25 men complete the remaining work in 6 days. how many days will it take for completing the entire job if only 15 women are put on the job?
Options- A. 60 days
- B. 88 days
- C. 94 days
- D. None of these Discuss
Correct Answer: None of these
Explanation:
25 men and 15 women can complete, a piece of work in 12 days.
? Work done by them in 8 days = 8/12 = 2/3
Remaining work is completed by 25 men in 6 days
? Time taken by 25 men to complete the whole work = 3 x 6 = 18 days
From the question
Time taken by 15 women to complete the whole work = 1 / (1/12 - 1/18)
= 1 / {(3 - 2) / 36} = 36/(3 - 2) = 36 days
- 6. A can do a piece of work in 12 days, B can do the same work in 8 days and c can do the same job in 4 / 5 th time required by both A and B. A and B work together for 3 days, then C complete days did C work?
Options- A. 8
- B. 6
- C. 3
- D. None of these Discuss
Correct Answer: None of these
Explanation:
As per question, work of A for 1 day = 1/12 and work of B for 1 day = 1/8
? Work of (A + B) together for 1 day = 1/12 + 1/8 = (2 + 3)/24 = 5/24
? Work of (A + B) together for 3 days = 3 x (5/24) = 5/8
? Remaining work after 3 days = 1 - 5/8 = 3/8
? C can do the same work in = 4/5th time required by (A + B) = 4/5 x 24/5 = 96/25 days
? Work of C for 1 day = 25/96 part.
? 25/96 part work can be done by C in 1 day
? 3/8 part work can be done by C in = 96/25 x 3/8 days = 36/25 days = 111/25
? The complete day C did the work = 1 day.
- 7. A completes a work in 15 days. B complete the same work in 20 days. A started working alone after 1 days B joined him. How many day will they now take together to complete the remaining work?
Options- A. 8 days
- B. 7 days
- C. 6 days
- D. None of these Discuss
Correct Answer: 8 days
Explanation:
Work of A for 1 day = 1/15
Work of B for 1 day = 1/20
Work of (A + B) together for 1 day = 1/15 + 1/20 = (4 + 3)/60 = 7/60
Remaining work after A alone does for 1 day = 1 - 1/15 = 14/15
? 7/60 part-work can be complete by (A + B) in 1 days
? 14/15 part-work can be completed by (A + B) in = (60/7) x (14/15) = 8 days.
- 8. A can do a piece of work in 10 days and B can do the same piece of work in 20 days. They start the work together but after 5 days A leaves off, B will do the remaining piece of work in?
Options- A. 5 days
- B. 6 days
- C. 8 days
- D. 10 days Discuss
Correct Answer: 5 days
Explanation:
(A + B)'s 5 day's work = 5 x (1/10 + 1/20) = 3/4
Remaining work = (1 - 3/4) = 1/4
1/20 work is done by B in = 1 day
? 1/4 work is done by B in = 20 x (1/4) i.e., 5 days.
- 9. Twelve men can complete a work in 8 days. Three days after they started the work, 3 more men joined them. In how, many days will all of them together complete the remaining work
Options- A. 2
- B. 4
- C. 5
- D. 6 Discuss
Correct Answer: 4
Explanation:
1 men's one day's work = 1/96
12 men's 3 day's work = 3 x (1/8) = 3/8
Remaining work = (1 - 3/8) = 5/8
15 men's 1 day's work = 15/96
Now, 15/96 work is done by them in 1 day
? 5/8 work will be done by them in = (96/15) x (5/ 8) i.e., 4 days
- 10. A can complete a job in 9 days, B in 10 days and C in 15 days. B and C start the work and are forced to leave after 2 days. The time taken to complete the remaining work is?
Options- A. 6 days
- B. 9 days
- C. 10 days
- D. 13 days Discuss
Correct Answer: 6 days
Explanation:
(B + C)'s 2 day's work = 2 x (1/10 + 1/15) = 1/3
Remaining work = (1 - 1/3) = 2/3
? 1/9 work is done by A in 1 day
? 2/3 work is done by A in (9 x 2) / 3 = 6 days
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