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A and B can complete a piece of work in 45 and 40 days respectively. Both started to work together, but after some days A left and B alone completed the rest work in 23 days. For how many days did A work?
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- 12 days
- 10 days
- 8 days
- 9 days
Correct Option: D
Using Rule 2,
Let A worked for x days.
| A’s 1 day’s work = | 45 |
| ∴ A’s x day’s work= | 45 |
| B’s 1 day’s work = | 40 |
∴ B’s x day’s work
| = | × x = | |||
| 40 | 40 |
(A + B) together worked for x days.
∴ (A + B)’s x day’s work
| = | + | |||
| 45 | 40 |
| = | = | |||
| 360 | 360 |
∴ Remaining work
| = 1 - | = | |||
| 360 | 360 |
This part of work, i.e.,
| 360 |
is completed by B alone in 23 days.
| ∴ | = 23 × B’s 1 day’s work | 360 |
| 360 |
| = 23 × | = | |||
| 40 | 40 |
∴ 360 – 17x
| = | × 360 = 207 | 40 |
∴ 17x = 360 – 207 = 153
| ⇒ x = | = 9 days | 17 |
Hence, A worked for 9 days.
