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Question:

P takes twice as much time as Q or thrice as much time as R to finish a piece of work. Working together, they can finish the work in 5 days. Q can do the work alone in

Explanation:

Let the time taken by P alone be 6x days.
∴ Time taken by Q alone will be 3x days and that by R will be 2x days.

Working together the three of them can finish the work in 5 days.

⇒ $\frac{1}{5} = \frac{1}{P} + \frac{1}{Q} + \frac{1}{R}$

⇒ $\frac{1}{5} = \frac{1}{6 x} + \frac{1}{3 x} + \frac{1}{2 x}$

⇒ $\frac{1}{5} = \frac{1 + 2 + 3}{6 x}$

⇒ $\frac{1}{5} = \frac{1}{x}$

⇒ x = 5

∴ Q alone can complete the work in 3x = 15 days.

Hence, option (c).

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