Time and Work
- A can do a piece of work in 20 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in
-
View Hint View Answer Discuss in Forum
Work done by B in 9 days
= 9 = 3 part 12 4
Remaining work= 1 - 3 = 1 4 4
which is done by A∴ Time taken by A = 1 × 20 = 5 days. 4 Correct Option: A
Work done by B in 9 days
= 9 = 3 part 12 4
Remaining work= 1 - 3 = 1 4 4
which is done by A∴ Time taken by A = 1 × 20 = 5 days. 4
- A, B and C can do a piece of work in 30, 20 and 10 days respectively. A is assisted by B on one day and by C on the next day, alternately. How long would the work take to finish ?
-
View Hint View Answer Discuss in Forum
Work done in first two days
= 2 + 1 + 1 30 20 10 = 1 + 1 + 1 15 20 10 = 4 + 3 + 6 = 13 60 60 Work done in first 8 days = 52 60
Remaining work= 1 - 52 = 8 = 2 60 60 15
(A + B)’s 1 day’s work= 1 + 1 = 2 + 3 = 3 30 20 60 12 ∴ Remaining work = 2 - 1 15 12 = 8 - 5 = 3 = 1 60 60 20
(A + C)’s 1 day’s work= 1 + 1 = 1 + 3 = 2 30 10 30 15 ∴ Time taken = 1 × 15 20 2 = 3 day 8 Total time = 9 + 3 = 9 3 days 8 8 Correct Option: A
Work done in first two days
= 2 + 1 + 1 30 20 10 = 1 + 1 + 1 15 20 10 = 4 + 3 + 6 = 13 60 60 Work done in first 8 days = 52 60
Remaining work= 1 - 52 = 8 = 2 60 60 15
(A + B)’s 1 day’s work= 1 + 1 = 2 + 3 = 3 30 20 60 12 ∴ Remaining work = 2 - 1 15 12 = 8 - 5 = 3 = 1 60 60 20
(A + C)’s 1 day’s work= 1 + 1 = 1 + 3 = 2 30 10 30 15 ∴ Time taken = 1 × 15 20 2 = 3 day 8 Total time = 9 + 3 = 9 3 days 8 8
- X alone can complete a piece of work in 40 days. He worked for 8 days and left. Y alone completed the remaining work in 16 days. How long would X and Y together take to complete the work ?
-
View Hint View Answer Discuss in Forum
Part of the work done by X in 8 days
= 8 = 1 40 5 ∵ work done in 1 day = 1 40 ∴ Remaining work = 1 - 1 = 4 5 5
This part of work is done by Y in 16 days.
∴ Time taken by Y in doing 1 work= 16 × 5 = 20 days. 4
∴ Work done by X and Y in 1 day= 1 + 1 = 1 + 2 = 3 40 20 40 40 Correct Option: A
Part of the work done by X in 8 days
= 8 = 1 40 5 ∵ work done in 1 day = 1 40 ∴ Remaining work = 1 - 1 = 4 5 5
This part of work is done by Y in 16 days.
∴ Time taken by Y in doing 1 work= 16 × 5 = 20 days. 4
∴ Work done by X and Y in 1 day= 1 + 1 = 1 + 2 = 3 40 20 40 40
- A and B can do a piece of work in 12 days and 15 days respectively. They began to work together but A left after 4 days. In how many more days would B alone complete the remaining work ?
-
View Hint View Answer Discuss in Forum
Part of the work done by A and B in 4 days
= 4 
1 + 1 
= 4 5 + 4 12 15 60 = 4 × 9 = 3 60 5 Remaining work = 1 - 3 = 2 5 5
∴ Time taken by B to complete the remaining work= 2 × 15 = 6 days 5
Aliter :
Using Rule 20,
Here, m = 12, n = 15, p = 4
B alone do the works in= mn - p(m + n) m = 12 × 15 - 4(12 + 15) 12 = 180 - 108 = 72 = 6 days 12 12 Correct Option: C
Part of the work done by A and B in 4 days
= 4 1 + 1 = 4 5 + 4 12 15 60 = 4 × 9 = 3 60 5 Remaining work = 1 - 3 = 2 5 5
∴ Time taken by B to complete the remaining work= 2 × 15 = 6 days 5
Aliter :
Using Rule 20,
Here, m = 12, n = 15, p = 4
B alone do the works in= mn - p(m + n) m = 12 × 15 - 4(12 + 15) 12 = 180 - 108 = 72 = 6 days 12 12
- A and B together can complete a work in 12 days. A alone can complete in 20 days. If B does the work only half a day daily, then in how many days A and B together will complete the work ?
-
View Hint View Answer Discuss in Forum
B’s 1 day's work
= 1 - 1 = 5 - 3 = 1 12 20 60 30 ∴ B's 1 day's work = 1 2 60
∴ (A + B)'s 1 day's work= 1 + 1 = 3 + 4 = 1 20 60 60 15
[ ∵ B works for half day daily]
Hence, the work will be completed in 15 days.Correct Option: D
B’s 1 day's work
= 1 - 1 = 5 - 3 = 1 12 20 60 30 ∴ B's 1 day's work = 1 2 60
∴ (A + B)'s 1 day's work= 1 + 1 = 3 + 4 = 1 20 60 60 15
[ ∵ B works for half day daily]
Hence, the work will be completed in 15 days.
