DIRECTION for the question: Solve the following question and mark the best possible option. A bath can be filled by the cold water pipe in 10 minutes and by the hot water pipe in 15 minutes. A person leaves the bathroom after turning on both the pipes. He returns just when the bath should have been full. Finding, however, the waste pipe was open, he closes it. In 4 minutes more, the bath is full. In what time will the waste water pipe empty it?

The combined filling rate of the hot and cold water pipes is 1/10 + 1/15 = 5/30, or 1/6 of the bath per minute, meaning the bath should have been full in 6 minutes. After 6 minutes with the waste pipe open, the remaining 4 minutes of filling at a rate of 1/6 per minute accounts for 4/6, or 2/3, of the bath. This means only 1/3 of the bath was filled during the initial 6 minutes, so the combined rate with all three pipes open was 1/18 per minute. Subtracting the filling rate of 1/6 from this net rate of 1/18 gives a waste pipe emptying rate of 1/6 - 1/18 = 2/18, or 1/9. The waste water pipe will empty the bath in 9 minutes.

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