Time and Work
- 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 ?
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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.
- A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately with A beginning, the work would be completed in
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Part of work done by A and B in first two days
= 1 + 1 = 4 + 3 = 7 9 12 36 36
Part of work done in first 10 days = 35/36Remaining work = 1 - 35 = 1 36 36
Now it is the turn of A.
∴ Time taken by A= 1 × 9 = 1 days 36 4
+= 10 1 4 10∴ Total time = 10 + 1 = 10 1 days 4 4 Correct Option: C
Part of work done by A and B in first two days
= 1 + 1 = 4 + 3 = 7 9 12 36 36
Part of work done in first 10 days = 35/36Remaining work = 1 - 35 = 1 36 36
Now it is the turn of A.
∴ Time taken by A= 1 × 9 = 1 days 36 4
+= 10 1 4 10∴ Total time = 10 + 1 = 10 1 days 4 4
- A alone can complete a work in 18 days and B alone in 15 days. B alone worked at it for 10 days and then left the work. In how many more days, will A alone complete the remaining work ?
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Part of work done by B in 10 days
= 10 × 1 = 2 15 3 Remaining work = 1 - 2 = 1 3 3 ∴ Time taken by A = 1 × 18 = 6 days 3 Correct Option: C
Part of work done by B in 10 days
= 10 × 1 = 2 15 3 Remaining work = 1 - 2 = 1 3 3 ∴ Time taken by A = 1 × 18 = 6 days 3
- 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
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(B + C)’s 2 days’ work
= 2 1 + 1 = 2 3 + 2 30 20 60 = 1 part 6 Remaining work = 1 - 1 = 5 part 6 6
∴ Time taken by A to complete this part of work= 5 × 18 = 15 days 6 Correct Option: C
(B + C)’s 2 days’ work
= 2 1 + 1 = 2 3 + 2 30 20 60 = 1 part 6 Remaining work = 1 - 1 = 5 part 6 6
∴ Time taken by A to complete this part of work= 5 × 18 = 15 days 6
- A and B alone can complete work in 9 days and18 days respectively. They worked together; however 3 days before the completion of the work A left. In how many days was the work completed ?
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Let the work be completed in x days.
According to the question,
A worked for (x –3) days, while B worked for x days.∴ x - 3 + x = 1 9 18 ⇒ 2x - 6 + x = 1 ⇒ 3x - 6 = 18 18
⇒ 3x = 18 + 6 = 24∵ x = 24 = 8 days 3
Aliter :
Using Rule 8,
Here, x = 9, y = 18, m = 3Total time taken = (x + m)y x + y = (9 + 3) × 18 9 + 18 = 12 × 18 = 8 days 27 Correct Option: B
Let the work be completed in x days.
According to the question,
A worked for (x –3) days, while B worked for x days.∴ x - 3 + x = 1 9 18 ⇒ 2x - 6 + x = 1 ⇒ 3x - 6 = 18 18
⇒ 3x = 18 + 6 = 24∵ x = 24 = 8 days 3
Aliter :
Using Rule 8,
Here, x = 9, y = 18, m = 3Total time taken = (x + m)y x + y = (9 + 3) × 18 9 + 18 = 12 × 18 = 8 days 27