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?

Answer 1

man alone can do it in = 14 days

man's 1 day work = 1/14

woman alone can do it in = 16 days

woman's 1 day work = 1/16

man woman and child can do it in = 6 days

man woman and child 1 day work = 1/6

for 1 day child of work = 1/6 - 1/14 - 1/16

= (56 - 24 - 21) / 336

= 11/336

1 day work of child is 11/336

so child can do it in 336/11 = 30 6/11 days

Answer 2

the correct answer is 27.818181 or 306/11 days