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1. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?

A. 10 min. 20 sec.

B. 11 min. 45 sec.

C. 12 min. 30 sec.

D. 14 min. 40 sec.

Solution:

\begin{aligned} Part filled in 4 minutes \\ = 4 (\frac{1}{15} + \frac{1}{20}) = \frac{7}{15} \\ Remaining part = 1 - \frac{7}{15} = \frac{8}{15} \\ Part filled by B in 1 minute = \frac{1}{20} \\ ∴ \frac{1}{20} : \frac{8}{15} :: 1 : x \\ x = \frac{8}{15} \times 1 \times 20 \\ = 10 \frac{2}{3} min \\ = 10 min . 40 \sec . \\ ∴ The tank will be full in \\ = 4 min . + 10 min . + 40 \sec . \\ = 14 min . 40 \sec . \end{aligned}

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