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A man, a woman and a boy can complete a work in 20 days, 30 days and 60 days respectively. How many boys must assist 2 men and 8 women so as to complete the work in 2 days ?
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- 8
- 12
- 4
- 6
Correct Option: A
Part of work done by 2 men and 2 women in 2 days.
| = 2 |  | + |  | 20 | 30 |
| = 2 | | + | | = 2 | | | 10 | 30 | 30 |
| = | = | |||
| 30 | 15 |
| Remaining work = 1 - | = | |||
| 15 | 15 |
Work done by 1 boy in 2 days
| = | = | |||
| 60 | 30 |
∴ Number of boys required to assist
| = | × 30 = 8 | 15 |
Aliter : Using Rule 14,
Here, A = 1, B = 1, C = 1
a = 20, b = 30, c = 60
A1 = 2, B1 = 8,
Required time
| = | |||||
| + | + | ||||
| A × a | B × b | C × c | |||
| 2 = | |||||
| + | + | ||||
| 1 × 20 | 1 × 30 | 1 × 60 | |||
| 2 = | |||||
| + | + | ||||
| 2 | 3 | 6 | |||
| 2 = | |
| 6 |
22 + x = 30 x = 8
∴ Number of boys = 8
