Discussion
Two pipes A and B can fill a tank in 12 minutes and 15 minutes respectively. if both the pipes are opened simultaneously and pipe A is closed after 3 minutes, then how much more time will it take to fill the tank by pipe B .. ?
Answer: D
Deal with the two stages separately. In the first 3 minutes both pipes run:
\[ 3\left(\frac{1}{12} + \frac{1}{15}\right) = 3 \times \frac{5 + 4}{60} = 3 \times \frac{9}{60} = \frac{9}{20} \]
That leaves \( 1 - \tfrac{9}{20} = \tfrac{11}{20} \) for B alone at \( \tfrac{1}{15} \) per minute:
\[ t = \frac{11/20}{1/15} = \frac{11}{20} \times 15 = \frac{33}{4} = 8\tfrac{1}{4} \text{ minutes} \]
which is 8 minutes 15 seconds, since a quarter of a minute is 15 seconds.
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