Question 70

Pipe P is twice as fast as Q, and Q is twice as fast as R. Find the ratio of the time taken by P, Q and R to fill a
cistern.

Solution

According to question,

$$2R_{speed}=Q_{speed\ }\ and\ \ P_{speed}=2Q_{speed}=4R_{speed}.$$

So,$$P_{time}:Q_{time}:R_{time}=\frac{1}{P_{speed}}:\frac{1}{Q_{speed}}:\frac{1}{R_{speed}}$$

$$=\frac{1}{4R_{speed}}:\frac{1}{2R_{speed}}:\frac{1}{R_{speed}}=\frac{1}{4}:\frac{1}{2}:\frac{1}{1}=1:2:4.$$

D is correct choice.

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Pipe P is twice as fast as Q, and Q is twice as fast as R. Find the ratio of the time taken by P, Q and R to fill acistern.