Question

A,B and C can do a piece of work in 10 days. A alone can do it in 40 days , B alone can do it in 30 days. In how many days will C alone do the same work.

Answer 1

A, B and C can do piece of work in 10 days

so they can do 1/10 part of work in a day

A alone can do same work in 40 days

so A can do 1/40 part of work in a day

B alone can do it in 30 days

so B can do 1/30 part of work in a day

let the days taken by C be x

1/10=1/40+1/30+1/x

1/10=7/120+1/x

1/10-7/120=1/x

12-7/120=1/x

5/120=1/x

1/24=1/x

therefore C can do 1/24 in a day

so C can do whole piece of work in 24 days

Answer 2

A, B, C in 1 day can do 1/10 work
A alone in 1 day can do 1/40 work
B alone in 1 day can do 1/30 work
C alone in 1 day can do 1/10-(1/40+1/30) work
C alone in one day can do 1/10-7/120 work
=5/120 work =1/24 work
Hence, C can do the whole work in 24 days