Time and Work
- A and B together can complete a work in 3 days. They start together. But, after 2 days, B left the work. If the work is completed after 2 more days, B alone could do the work in
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(A + B)’s 2 days’ work = 2 3 Remaining work = 1 - 2 = 1 3 3 Time taken by A in doing 1 work = 2 days 3
∴ Time taken by A in completing the work = 6 days∴ B’s 1 day’s work = 1 - 1 3 6 = 2 - 1 = 1 6 6
∴ B alone will complete the work in 6 days.Correct Option: C
(A + B)’s 2 days’ work = 2 3 Remaining work = 1 - 2 = 1 3 3 Time taken by A in doing 1 work = 2 days 3
∴ Time taken by A in completing the work = 6 days∴ B’s 1 day’s work = 1 - 1 3 6 = 2 - 1 = 1 6 6
∴ B alone will complete the work in 6 days.
- 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 ?
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(A + B + C)'s 1 day's work
= 1 + 1 + 1 20 30 60 = 3 + 2 + 1 = 1 60 10 A’s 2 days’ work = 2 = 1 20 10
Work done in first three days= 1 + 1 10 10 = 2 = 1 10 5
[A's work for 2 days + (A + B + C) work on 3rd day]
Hence, the work will be finished in 15 days.Correct Option: C
(A + B + C)'s 1 day's work
= 1 + 1 + 1 20 30 60 = 3 + 2 + 1 = 1 60 10 A’s 2 days’ work = 2 = 1 20 10
Work done in first three days= 1 + 1 10 10 = 2 = 1 10 5
[A's work for 2 days + (A + B + C) work on 3rd day]
Hence, the work will be finished in 15 days.
- A and B together can do a piece of work in 12 days which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days B could finish the work ?
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Let the work done by each one of A, B and C per day be x, y, and z respectively.
∴ x + y = 1 12 ⇒ x = 1 - y ..................(i) 12 y + z = 1 ⇒ z = 1 - y ..........(ii) 16 16
Again, 5x + 7y + 13z = 1⇒ 5 
1 - y 
+ 7y + 13 1 - y = 1 12 16 ⇒ 5 - 5y + 7y + 13 - 13y = 1 12 16 ⇒ 11y = 5 + 13 - 1 12 16 = 20 + 39 - 48 = 11 48 48 ⇒ y = 1 48
∴ B alone will complete the work in 48 daysCorrect Option: A
Let the work done by each one of A, B and C per day be x, y, and z respectively.
∴ x + y = 1 12 ⇒ x = 1 - y ..................(i) 12 y + z = 1 ⇒ z = 1 - y ..........(ii) 16 16
Again, 5x + 7y + 13z = 1⇒ 5 1 - y + 7y + 13 1 - y = 1 12 16 ⇒ 5 - 5y + 7y + 13 - 13y = 1 12 16 ⇒ 11y = 5 + 13 - 1 12 16 = 20 + 39 - 48 = 11 48 48 ⇒ y = 1 48
∴ B alone will complete the work in 48 days
- A can finish a work in 18 days and B can do the same work in 5 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
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Work done by B in 10 days
= 10 = 2 15 3 Remaining work = 1 - 2 = 1 3 3
∴ Time taken by A to complete the work= 1 × 18 = 6 days. 3 Correct Option: A
Work done by B in 10 days
= 10 = 2 15 3 Remaining work = 1 - 2 = 1 3 3
∴ Time taken by A to complete the work= 1 × 18 = 6 days. 3
- A can do a piece of work in 8 days which B can destroy in 3 days. A has worked for 6 days, during the last 2 of which B has been destroying; how many days must A now work alone to complete the work ?
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Work done by A in 6 days
= 6 = 3 part 8 4
Work destroyed by B in 2 days= 2 part 3
Remaining work after destruction= 3 - 2 = 9 - 8 = 1 4 3 12 12
Now, time taken by A in doing= 11 part 12 = 11 × 8 = 22 = 7 1 days 12 3 3 Correct Option: B
Work done by A in 6 days
= 6 = 3 part 8 4
Work destroyed by B in 2 days= 2 part 3
Remaining work after destruction= 3 - 2 = 9 - 8 = 1 4 3 12 12
Now, time taken by A in doing= 11 part 12 = 11 × 8 = 22 = 7 1 days 12 3 3
