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2 men and 3 women can do a piece of work in 4 days. 6 men and 1 woman can do the same work in 2 days. In how many days can 4 men and 6 women do the work?1. 2 days2. 4 days3. 3 days4. 5 days |
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Answer» Correct Answer - Option 1 : 2 days Given: 2 men and 3 women can do a piece of work in 4 days 6 men and 1 woman can do the same work in 2 days Concept used: Efficiency ∝ (1/Time) Calculation: Let men be m Let women be w Let x be the days 4 men and 6 women take to complete the work (2m + 3w) × 4 = (6m + 1w) × 2 ⇒ (2m + 3w) × 2 = (6m + 1w) × 1 ⇒ (4m + 6w) = (6m + 1w) ⇒ (6w – 1w) = (6m – 4m) ⇒ (5w) = (2m) ⇒ m : w = 5 : 2 Total work = [(2m + 3w) × 4] or [(6m + 1w) × 2] Taking one of them [(2m + 3w) × 4] ⇒ [{(2 × 5) + (3 × 2)} × 4] ⇒ [(10+ 6) × 4] ⇒ Total work = 64 (4m + 6w) × x = 64 ⇒ [(4 × 5) + (6 × 2)] × x = 64 ⇒ 32 × x = 64 ⇒ x = 2 ∴ 4 men and 6 women take to complete the work in 2 days. |
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