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A, B and C can complete a work in 8 days. B alone can do it in 18 days and C alone can do it in 24 days. In how many days can A alone do the same work?
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- 36 days
- 24 days
- 38 days
- 30 days
Correct Option: A
(A + B + C)’s 1 day’s work
| = | 8 |
| B’s 1 day’s work = | 18 |
| C’s 1 day’s work = | 24 |
∴ A’s 1 day’s work
= (A + B + C)’s 1 day’s work – B’s
1 day’s work – C’s 1 day’s work
| = | - | - | ||||
| 8 | 18 | 24 |
| = | = | = | ||||
| 72 | 72 | 36 |
| ⇒ A’s 1 day’s work = | 36 |
∴ A alone can do the same work in 36 days.
Aliter : Using Rule 18,
Here, x = 8, y = 18, z = 24
Required time
| = | zy - x(y + z) |
| = | 24 × 18 - 8(18 + 24) |
| = | 432 - 336 |
| = | = 36 days | 96 |
