Question

A, B and C working together can finish a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?

Answer 1

we know that,

Number of hours A required to do piece of work = 20 hours

Number of hour B required to do piece of work = 24 hours

Let us consider number of hours C required to do piece of work = x hours

Number of hours A,B and C together required to do piece of work = 8 hours

∴ We can calculate, work done by A in 1 hour = 1/20

Work done by B in 1 hour = 1/24

Work done by C in 1 hour = 1/x

Work done by A, B and C together in a one hour = 1/8

Now, work done by A,B and C together in 1 hour= 1/20 + 1/24 +1/x = 11/120 + 1/x

11/120 + 1/x = 1/8

(11x+120)/120x = 1/8

88x + 960 = 120x

32x = 960

x = 960/32 = 30

∴ C can do the work in 30 hours.