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A man is 4 times as fast as woman and a woman is twice as fast as a boy in doing a work. If 1 man, 1 woman and 1 boy working together can complete it in 6 days, in how many days a woman will do it alone?

A man is 4 times as fast as woman and a woman is twice as fast as a boy in doing a work. If 1 man, 1 woman and 1 boy working together can complete it in 6 days, in how many days a woman will do it alone? Correct Answer 33 days

Let, a boy’s efficiency = x/day

∴ A woman’s efficiency = 2 × x = 2x/day

∴ A man’s efficiency = 4 × 2x = 8x/day

Let, a woman can complete the work in = y days

According to problem,

⇒ (x + 2x + 8x) × 6 = 2x ×y

⇒ 66x = 2xy

⇒ 2y = 66

⇒ y = 33

∴ In 33 days a woman will complete the work.

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