Question

27.A,B and C working together can do 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?
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Answer 1

Answer:

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given that:-

Time taken by A,B and C when they work together=8 hrs

Time taken by A when he work alone=20 hrs

Time taken by B when he work alone=24 hrs

To find:-

Time taken by C when he work alone=?

Solution:-

Work done by A when he work alone=1/20

Work done by B when he work alone=1/24

Let the time taken by C when he work alone be x hrs and work done by C be 1/x

Work done by A,B and C when they work together=1/8

$\frac{1}{20} + \frac{1}{24} + \frac{1}{x} = \frac{1}{8} \\ \frac{1}{x} = \frac{1}{8} - \frac{1}{20} - \frac{1}{24} \\ \frac{1}{x} = \frac{60 - 24 - 20}{480} \\ \frac{1}{x} = \frac{16}{480} \\ \frac{1}{x} = \frac{1}{30} \\ x = 30 \: hrs$

Therefore, time taken by C when he work alone is 30 hrs.