Time and Work problems
- 1. P alone can complete a piece of work in 6 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together ?
Options- A. 5 (2/3)
- B. 6 (3/4 )
- C. 4 (1/2)
- D. 3 Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 4 (1/2)
Explanation:
Work done by P alone in one day = 1/6th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/6 of the total) = 1/18 of the total.
Work done by P and Q, working together in one day = 1/6 + 1/18 = 4/18 = 2/9
They would take 9/2 days = 4 (1/2) days to complete the work working together.
- 2. S, T and U together can complete a work in 30 days. If the ratio of efficiency of S, T and U is 20 : 15 : 12 respectively, then in how many days U alone can complete the same work?
Options- A. 195/2
- B. 235/2
- C. 225/2
- D. 215/2 Also asked in: Bank Exams
Correct Answer: 235/2
- 3. A and B together finish a wor in 20 days.They worked together for 15 days and then B left. Afer another 10 days,A finished the remaining work. In how many days A alone can finish the job?
Options- A. 30
- B. 40
- C. 50
- D. 60 Discuss
Correct Answer: 40
Explanation:
(A+B)'s 15 days work =
Remaining work = 1/4
Now, 1/4 work is done by A in 10 days.
Whole work will be done by A in (10 x 4) = 40 days.
- 4. Ten women can do a work in six days. Six men can complete the same work in five days. What is the ratio between the capacity of a man and a woman?
Options- A. 1:2
- B. 2:1
- C. 2:3
- D. 3:2 Discuss
Correct Answer: 2:1
Explanation:
(10 * 6) women can complete the work in 1 day.
Therefore, 1 woman's 1 day's work = 1/60
(6 * 5) men can complete the work in 1 day.
Therefore, 1 man's 1 day's work = 1/30
so, required ratio =1/30 : 1/60 = 2:1
- 5. A shopkeeper has a job to print certain number of documents and there are three machines P, Q and R for this job. P can complete the job in 3 days, Q can complete the job in 4 days and R can complete the job in 6 days. How many days the shopkeeper will it take to complete the job if all the machines are used simultaneously ?
Options- A. 4/3 days
- B. 2 days
- C. 3/2 days
- D. 4 days Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 4/3 days
Explanation:
Let the total number of documents to be printed be 12.
The number of documents printed by P in 1 day = 4.
The number of documents printed by Q in 1 day = 3.
The number of documents printed by R in 1 day = 2.
Thus, the total number of documents that can be printed by all the machines working simultaneously in a single day = 9.
Therefore, the number of days taken to complete the whole work = 12/9 = 4/3 days.
- 6. A can write 32 pages in 6 hours and B can write 40 pages in 5 hours. If they write together, in how many hours they can write 110 pages ?
Options- A. 7 hrs
- B. 6 hrs 10 min
- C. 5 hrs 25min
- D. 8 hrs 15 min Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 8 hrs 15 min
Explanation:
A can write in 1hour = 32/6 pages
Similarly, B in 1 hour = 40/5 pages
Together (A+B) in 1 hour = 32/6 + 40/5 = 40/3
So, A+B write 40/3 pages in 1 hour
A+B write 110 pages in (3/40) x 110 Hours = 8 hours 15 min.
- 7. A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in --- days ?
Options- A. 51/24
- B. 87/5
- C. 57/12
- D. 60/11 Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 60/11
Explanation:
A can complete the work in 12 days working 8 hours a day
=> Number of hours A can complete the work = 12×8 = 96 hours
=> Work done by A in 1 hour = 1/96
B can complete the work in 8 days working 10 hours a day
=> Number of hours B can complete the work = 8×10 = 80 hours
=> Work done by B in 1 hour = 1/80
Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480
=> A and B can complete the work in 480/11 hours
A and B works 8 hours a day.
Hence total days to complete the work with A and B working together
= (480/11)/ (8) = 60/11 days
- 8. A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in ?
Options- A. 3 hrs
- B. 6 hrs
- C. 7 hrs
- D. 5 hrs Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 6 hrs
Explanation:
Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/2
6/x = 1/2 => x = 12
So, B takes 6 hours to finish the work.
- 9. A work which could be finished in 11 days was finished 4 days earlier after 4 more men joined. The number of men employed was ?
Options- A. 7
- B. 8
- C. 9
- D. 10 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 7
Explanation:
As the work is same
M1D1 = M2D2
Here Let the number of men employed was M
=> 11M = 7(M+4)
=> 11M - 7M = 28
=> M = 7
- 10. A laborer is engaged for 30 days on the condition that he receives Rs.25 for each day he works and is fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was he absent ?
Options- A. 10 days
- B. 14 days
- C. 11 days
- D. 9 days Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 10 days
Explanation:
For 30 days he receives
30 x 25 = 750
Actually he gets 425
Therefore, Fine is 750 - 425 = 325
=> No of days absent = 325/(25+7.50)= 10
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