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Sixteen men can finish a work in 8 days. Eight men and nine women working together can finish the same work in 10 days. In how many days will twenty women finish the same work?

Sixteen men can finish a work in 8 days. Eight men and nine women working together can finish the same work in 10 days. In how many days will twenty women finish the same work? Correct Answer 12

Let the efficiency of 1 man and 1 woman are x and y respectively

According to the question

16m × 8 = (8m + 9w) × 10

⇒ 128m = 80m + 90w

⇒ 128m – 80m = 90w

⇒ 48m = 90w

m : w = 15 : 8

Total work  = 16 × 15 × 8

Let 20 women complete the whole work in x days,

⇒ 20 × 8 × x = 16 × 15 × 8

⇒ x = 12 days

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