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 cando it in 24 hours. In how many hours will C alone doth same work?​

Answer 1

Answer:

30 hours

Step-by-step explanation:

A, B & C working together to finish a work = 8 hours

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

A alone can finish the work = 20 hours

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

B alone can finish the work = 24 hours

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

Work done by C in 1 hour= $\frac{1}{8} -(\frac{1}{20} +\frac{1}{2} =\frac{1}{8} -\frac{(6+5)}{120} )$

= $\frac{1}{8} -(\frac{11}{20})$

= $(\frac{(15-11)}{120} )$

= $\frac{4}{20}$

= $\frac{1}{30}$

∴C alone can do the same work in 1÷ 1/30= 1× 30 = 30 hours.

Hence, C alone can do the same work in 30 hours.

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