Question 75

A, B and C are three pipes attached to a cistern. A and B can fill it in 20 minutes and 30 minutes respectively, while C can empty it in 15 minutes. If A, B and C be kept open successively for 1 minute each, how soon will the cistern be filled?

Solution

Part filled by A, B and emptied by C in one minute = $$\frac{1}{20}, \frac{1}{30}$$ and $$\frac{1}{15}$$

Part filled by three pipes in 3 minutes = $$\frac{1}{20} + \frac{1}{30}$$ - $$\frac{1}{15}$$

$$\Rightarrow \frac{3 + 2 - 4}{60} = \frac{1}{60}$$

Cistern can be filled in 60 x 3 = 180 minutes.

Hence, option A is the correct answer.

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