Question

A man, a women and a child can do a piece of work in 6 days, man can do it in 14 days, women can do it 16 days, and in how many days child can do the same work? apti

Answer 1

The man takes 14 days to complete the work. So work done by him in one day = 1/14.

The woman takes 16 days. So work done by her in a day = 1/16.

Child takes C days. So work done in one day = 1/C.

Adding work done by the man, woman and the child together in a day = (1/14) + 1/(16) + (1/C).

All three together take 6 days. So in a day, total work done = 1/6.

Equating the two points.

(1/14) + (1/16) + (1/C) = 1/6

Multiply by 6.

(3/7) + (3/8) + (6/C) = 1

Multiply by 56.

24 + 21 + (336/C) = 56

336/C = 11

C= 336/11 ~ 30.5 days.

The child takes 30.5 days to complete the work alone.