2 men and 3 women undertook a piece of work for Rs. 12,000. 2 men can do the work in 12 days and 3 women can do the same work in 15 days. With the assistance of 5 children, they finished the work in 5 days. What is the share of 1 child?
1). 500
2). 400
3). 300
4). 600
Work done by 2 men in 1 day = 1/12
Work done by 3 women in 1 day = 1/15
Work done by (2 men + 3 women + 5 children) in 1 day = 1/5
∴ Work done by 5 children in 1 day = 1/5 – 1/12 – 1/15 = 1/20
⇒ 5 children alone can do the work in 20 days
Ratio of their time (2 Men ? 3 Women ? 5 Children) = 12 ? 15 ? 20
We know, efficiency is inversely proportional to the time
∴ Ratio of their efficiency (2 Men ? 3 Women ? 5 Children) = 1/12 ? 1/15 ? 1/20 = 5 ? 4 ? 3
So, 5 + 4 + 3 = 12 unit = 12000
⇒ 3 unit = 3000
⇒ Share of 5 children is 3000
∴ Share of 1 child = 3000/5 = 600