3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days? Correct Answer 7

Given∶

Time taken by 3 men, 4 women, 6 children to complete the work = 7 days.

A woman does double work compare to a man and a child does half work compare to a man.

Ratio of efficiency of man and woman = 1 ∶ 2,

Ratio of efficiency of child and man = 1 ∶ 2

Calculation∶

Ratio of efficiency of man, woman and child = 2 ∶ 4 ∶ 1

Total work = (3 man + 4 woman + 6 child) × 7 days = (3 × 2 + 4 × 4 + 6 × 1) × 7 = 28 × 7 = 196