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A 10 hectare field is reaped by 2 men, 3 women and 4 children together in 10 days. If working capabilities of a man, a woman and a child are in the ratio 5 : 4 : 2, then a 16 hectare field will be reaped by 6 men,4 women and 7 children in
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- 5 days
- 6 days
- 7 days
- 8 days
Correct Option: D
Using Rule 1,
Ratio of the working capabilities of a man, a woman and a child = 5 : 4 : 2
∴ Ratio of man, woman and child equivalence
| = | : | : | ||||
| 5 | 4 | 2 |
| = | × 20 : | × 20 : | × 20 | |||
| 5 | 4 | 2 |
= 4 : 5 : 10
or 4 men ≡ 5 women ≡ 10 children 4 men = 10 children
∴ 2 men ≡ 5 children and 6 men ≡ 15 children
5 women = 10 children
∴ 3 women ≡ 6 children
4 women ≡ 8 children
∴ 2 men + 3 women + 4 Children = 15 children
6 men + 4 women + 7 children = 30 children
where, x is no. of days
⇒ 30 × 10 × x = 15 × 16 × 10
| ⇒ x = | = 8 days | 30 × 10 |
