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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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- 48 days
- 24 days
- 16 days
- 12 days
Correct Option: A
Let the work done by each one of A, B and C per day be x, y, and z respectively.
| ∴ x + y = | 12 |
| ⇒ x = | - y ..................(i) | 12 |
| y + z = | ⇒ z = | - y ..........(ii) | ||
| 16 | 16 |
Again, 5x + 7y + 13z = 1
| ⇒ 5 |  | - y |  | + 7y + 13 | | - y | | = 1 | 12 | 16 |
| ⇒ | - 5y + 7y + | - 13y = 1 | ||
| 12 | 16 |
| ⇒ 11y = | + | - 1 | ||
| 12 | 16 |
| = | = | |||
| 48 | 48 |
| ⇒ y = | 48 |
∴ B alone will complete the work in 48 days
