P and Q together can fill a cistern with water in 15 hours. If P alone can fill the cistern with water in 60 hours, then in how many hours will Q alone fill one-fourth of the same cistern with water?
5
Rate of (P + Q) together = \(\dfrac{1}{15}\) cistern/hour. Rate of P alone = \(\dfrac{1}{60}\) cistern/hour.
Rate of Q alone = \(\dfrac{1}{15} - \dfrac{1}{60} = \dfrac{4-1}{60} = \dfrac{3}{60} = \dfrac{1}{20}\) cistern/hour.
Q alone fills the full cistern in 20 hours. To fill \(\dfrac{1}{4}\) of the cistern: \(\dfrac{1}{4} \times 20 = 5\) hours.
The correct answer is : 5.
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