Question 74

A bath can be filled by the cold water and hot water pipes in 10 minutes and 15 minutes respectively. A person leaves the bathroom after turning on both pipes simultaneously and returns at the moment when the bath should be full. Finding, however, that the waste pipe has been open, he then closes it. In exactly four minutes more the bath is full. In how much time would the waste pipe empty the full bath, if it alone is opened?

Solution

Time taken by the hot and cold water pipes to fill the bath,

= $$\frac{10 \times 15}{10 + 15} = 6$$ min

Total time taken to fill the bath including the empty pipe is also open = (6 + 4) = 10 min

Let '$$x$$' be the time taken by empty pipe to empty the bath.

$$\therefore \frac{1}{10} + \frac{1}{15} + \frac{1}{x} = \frac{1}{10}$$

$$\Rightarrow \frac{1}{x} = \frac{1}{15}$$

$$\Rightarrow x = 15$$ min

Hence, option D is the correct answer.

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