Question

A man and a boy complete a work together in 24 days.if for the last 6 day man alone does the work then it is completed in 26 dyays. how long the boy will take to complete the work

Answer 1

man and boy together do a job in 24 days;therefore in one day they do 1/24part of work; m+b=1/24...(i)

man and boy together work for first 18 days (as the last 6 days man works alone); therefore in 18 days they do 18/24 part of work; i.e.3/4 part of work; therefore work remianing is 1-3/4=1/4

Therefore man does 1/4 of the work in 8 days (26-18); therefore man can alone do the whole work in 32 days; therefore man does 1/32 part of work in one day.

substituting the value of m in equation (i) we get 1/32+b=1/24

b=1/24-1/32

b=1/96

Therefore boy can alone do in 96 days