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If number of men is 25% less than the number of women and number of boys is 50% more than the number of women. If number of women is 4. All together they can complete a work in 8 days. A man does double the work a woman does and a boy does half the work a woman does in a day. How many boys can complete 25% of this work in 13 days?

If number of men is 25% less than the number of women and number of boys is 50% more than the number of women. If number of women is 4. All together they can complete a work in 8 days. A man does double the work a woman does and a boy does half the work a woman does in a day. How many boys can complete 25% of this work in 13 days? Correct Answer 4

Total number of women is 4.

Number of men = 4 × = 3

Number of boys = 4 × = 6

3 men, 4 women and 6 boys together can complete a work in 5 days

According to the question

⇒ 2W = M

⇒ M ∶ W = 2 ∶ 1      ----(1)

⇒ B = W/2

⇒ W ∶ B = 2 ∶ 1      ----(2)

Multiply by 2 in equation (1)

Efficiency of man, woman and boy (M ∶ W ∶ B) = 4 ∶ 2 ∶ 1

Total work = (3M + 4W + 6B) × 8 = (3 × 4 + 4 × 2 + 6 × 1) × 8 = 208

Let x boys alone can complete 25% of the total work in 13 days, then

⇒ x × 1 × 13 = 208 × = 52

⇒ x = 4 days

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