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4 men and 6 women complete a work in 8 days. 2 men and 9 women also complete in 8 days in which. The number of days in which 18 women complete the work is :
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4 1 days 3 -
5 1 days 3 -
4 2 days 3 -
5 2 days 3
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Correct Option: B
According to the question,
(4 × 8) men + (6 × 8) women ≡ (2 × 8) men + (9 × 8) women
⇒ 4 men + 6 women ≡ 2 men + 9 women
⇒ (4 – 2) men ≡ (9 – 6) women
⇒ 2 men ≡ 3 women
∴ 4 men + 6 women ≡ 12 women
∴ M1D1 = M2D2
⇒ 12 × 8 = 18 × D2
| ⇒ D2 = | 18 |
| = | = 5 | days | ||
| 3 | 3 |
Aliter : Using Rule 1,
Here, A1 = 4, B1 = 6, D1 = 8
A2 = 2, B2 = 9, D2 = 8
A3 = 0, B3 = 18
Required time
| = | ||
| D1(A1B3 - A3B1) - D2(A2B3 - A3B2) |
| = | 8(4 × 18 - 0 × 6) - 8(2 × 18 - 0 × 6) |
| = | = | |||
| 8 × 72 - 36 × 8 | 36 |
| = | = 5 | days | ||
| 3 | 3 |
