Question

A and B can do a piece of work in 18 days B and C in 24 days and A and C in 36 days in what time can they do it, all working together?

Answer 1

they work together in 8days

Answer 2

A + B in 18 days = 1 (piece of work)
" " in 1 day = 1/18 (piece of work) -- (1)
Again,
B+C in 24 days = 1 (piece of work)
B+C in 1 day = 1/24 (piece of work) -- (2)
And, A+C in 36 days = 1 (piece of work)
A+C in 1 day = 1/36 (piece of work) --- (3)
Adding (1),(2),(3) we get
2(A+B+C) in 1 day =(1/18 + 1/24 +1/36) (piece of work)
= A+B+C in 1 day = 1/(8*2) (piece of work)
A+B+C in 1 day = 1/16 (piece of work)
Hence A + B + C together in 16 days can do a piece of work.