Question

A can do a piece of work in 24 hours while B alone can do it in 16 hours. If A, B and C working together can finish it in 8 hours, in how many hours can C alone finish the work?

Answer 1

we know that,

Number of hours A required to do piece of work = 24 hours

Number of hour B required to do piece of work = 16 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 = 1/24

Work done by B in 1 hour = 1/16

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= 1/24 + 1/16 +1/x = 5/48 + 1/x

5/48 + 1/x = 1/8

(5x+48)/48x = 1/8

40x + 384 = 48x

8x = 384

x = 384/8 = 48

∴ C can do the work in 48 hours.