Sixteen men can complete a work in fifteen days, twenty four children can do the same work in twenty days. In how many days will eight men and eight children, complete the same work?

Sixteen men can complete a work in fifteen days, twenty four children can do the same work in twenty days. In how many days will eight men and eight children, complete the same work? Correct Answer 20 days

We have 16 men completing the work in 15 days.

Time taken by 1 man to complete the entire work = 16 × 15 = 240 days.

Hence, part of work done by a man in 1 day = 1/240.

We have 24 children doing the work in 20 days.

Hence, time taken by 1 child to complete the entire work alone = 24 × 20 = 480 days.

Hence, part of work done by a child in a day = 1/480.

Let number of days taken by 8 men and 8 children to complete the work be n.

We have

⇒ n × 8 × = 1

⇒ n × 8 × (3/480) = 1.

⇒ n/20 = 1

⇒ n = 20