Question

A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days. In how many days can A, B, C finish it, if they all work together?

Answer 1

Number of days required by A and B to finish the work : 18 days 

Number of days required by A and B to finish the work : 24 days 

Number of days required by A and B to finish the work : 36 days

Work done by A and B in one day: \(\frac{1}{18}\)

Work done by B and C in one day: \(\frac{1}{24}\)

Work done by C and A in one day: \(\frac{1}{36}\)

Work done by (A and B) , (B and C ) and (C and A) in one day that is work done by

(A + B) + (B + C) + (C + A) = 2(A + B + C) = \(\frac{1}{18}+\frac{1}{24}+\frac{1}{36}=\frac{9}{72}=\frac{1}{8}\)

Work done by A, B and C = \(\frac{1}{2}\times\frac{1}{8}=\frac{1}{16}\)

∴ They can do the work in 16 days