vA, B and C working together can finish a piece of work in 8 hours.
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?

Solution:

A can complete the work in $20 \mathrm{~h}$.

Work done per hour by A $=\frac{1}{20}$

B can complete the work in $24 \mathrm{~h} .$

Work done per hour by B $=\frac{1}{24}$

It takes $8 \mathrm{~h}$ to complete the work if A, B and C work together.

Work done together per hour by A,B and C $=\frac{1}{8}$

(Work done per hour by A, B and C) $=($ work done per hour by A) $+($ work done per hour by B)$+($ work done per hour by C)

OR

(Work done per hour by C) $=($ work done per hour by A, B and C) $-($ work done per hour by A)$-($ work done per hour by B)

$=\frac{1}{8}-\frac{1}{24}-\frac{1}{20}=\frac{1}{30}$

$\therefore$ C alone will take $30 \mathrm{~h}$ to complete the work.

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