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2 men, 3 women and 5 boys together can complete a work in 10 days. A man does double the work a woman does and a woman does double the work a boy does. How many boys alone can complete 50% of the total work in 5 days?

2 men, 3 women and 5 boys together can complete a work in 10 days. A man does double the work a woman does and a woman does double the work a boy does. How many boys alone can complete 50% of the total work in 5 days? Correct Answer 19

2 men, 3 women and 5 boys together can complete a work in 10 days

According to the question

A man does double the work a woman does.

M = 2W

M : W = 2 : 1

Efficiency ratio of one man to one woman = 2 : 1      ----(1)

A woman does double the work a boy does.

W = 2B

W : B = 2 : 1

Efficiency ratio of one woman to one boy = 2 : 1      ----(2)

Multiply by 2 in equation (1)

Efficiency ratio of one man, one woman and one boy = 4 : 2 : 1

Total work = (2M + 3W + 5B) × 10 = (2 × 4 + 3 × 2 + 5 × 1) × 10 = (8 + 6 + 5) × 10 = 19 × 10 = 190

50% of the total work = 190 × = 190 × 1/2 = 95

Let x boys complete the 50% of the work in 5 days, then

x × B × 5 = 95

⇒ x × 1 × 5 = 95

⇒ x = 19 Boys

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