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A and B can do a given piece of work in 8 days, B and C can do the same work in 12 days and A, B, C complete it in 6 days. Number of days required to finish the work by A and C is
-
- 16
- 8
- 12
- 24
Correct Option: B
| (A + B)’s 1 day’s work = | 8 |
| (B + C)’s 1 day’s work = | 12 |
| (A + B + C)’s 1 day’s work = | 6 |
| ∴ C’s 1 day’s work = | - | |||
| 6 | 8 |
| = | = | |||
| 24 | 24 |
A’s 1 day’s work
| = | - | = | = | |||||
| 6 | 12 | 12 | 12 |
∴ (A + C)’s 1 day’s work
| = | + | = | = | |||||
| 12 | 24 | 24 | 8 |
∴ Required time = 8 days
Aliter : Using Rule 5,
Let the time taken by A and C is x days
| ⇒ 6 = | 8x + 96 + 12x |
| 6 = | 20x + 96 |
120x + 576 = 192x
72x = 576
x = 8 days
