Question

A and B can do apiece of work in 30 days ; B and C in 24 days ; C and A in 40 days. How long will it take them do finish it together

Answer 1

A+B finishes the work in 30days

part of the work (A+B ) finishes in 1 day = 1/30
similarly,
part of the work (B+C) finishes in 1 day = 1/24
part of the work (C+A) finishes in 1 day = 1/40

part of the work (A+B) +(B+C)+(C+A) finishes in 1 day = 1/30 +1/24+ 1/40

2(A+B+C) = (4+5+3)/120

= 12/120
=1/10
A+B+C = 1/20

therefore
part of the workA,B and C all the three finishes in 1 day = 1/20

all three completes the work in 20 days