Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. Both pipes A and B are opened together for some time and then pipe B is turned off. If the tank is filled in 15 minutes, then time for which the pipe B works is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(7\displaystyle\frac{1}{2}\) minutes
Let pipe B work for t minutes. Pipe A works for the whole 15 minutes. In one minute A fills \(\frac{1}{20}\) and B fills \(\frac{1}{30}\) of the tank, and together they fill the whole tank:
\( \displaystyle \frac{15}{20} + \frac{t}{30} = 1 \)
\( \displaystyle \frac{t}{30} = \frac{1}{4} \)
\( \displaystyle t = \frac{30}{4} = 7\frac{1}{2} \text{ minutes} \)