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3 men, 4 women and 6 boys together can complete a work in 6 days. A woman does triple the work a man does and a boy does half the work a man does. How many women alone will be able to complete this work in 4 days?

3 men, 4 women and 6 boys together can complete a work in 6 days. A woman does triple the work a man does and a boy does half the work a man does. How many women alone will be able to complete this work in 4 days? Correct Answer 9

3 men, 4 women and 6 boys together can complete a work in 6 days

According to the question

⇒ W = 3M

⇒ M : W = 1 : 3

⇒ B = M/2

⇒ M : B = 2 : 1

Efficiency of man, woman and boy (M : W : B) = 2 : 6 : 1

Total work = (3M + 4W + 6B) × 6

⇒ (3 × 2 + 4 × 6 + 6 × 1) × 6 = 216

Suppose x women alone can complete that work in 4 days, then

⇒ x × 6 × 4 = 216

⇒ x = 9 days

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