Question

Two pipes A and B can fill a cistern in 15 minutes and 30 minutes respectively. Both pipes are opened together, but after 5 minute pipe B is turned off. The cistern will be full in total:

• A. 10 minutes
• B. 7.5 minutes
• C. 15 minutes
• D. 12.5 minutes

Answer 1

The Correct Option is D

To solve the problem, we need to calculate the total time taken by both pipes A and B to fill the cistern with the condition that pipe B is turned off after 5 minutes.

First, let's determine their individual rates of filling the cistern:

• Pipe A takes 15 minutes to fill the cistern. Thus, its rate is \( \frac{1}{15} \) of the cistern per minute.
• Pipe B takes 30 minutes to fill the cistern. Thus, its rate is \( \frac{1}{30} \) of the cistern per minute.

When both pipes are opened together for the first 5 minutes, their combined rate is:

\(\frac{1}{15} + \frac{1}{30} = \frac{2}{30} + \frac{1}{30} = \frac{3}{30} = \frac{1}{10}\)

So, in 5 minutes, they fill:

\(\frac{1}{10} \times 5 = \frac{5}{10} = \frac{1}{2}\) of the cistern.

After 5 minutes, pipe B is turned off, and only pipe A continues to fill the cistern. At this point, half of the cistern is already filled, so half remains. Pipe A will take additional time to fill the remaining cistern:

Pipe A fills \(\frac{1}{15}\) of the cistern per minute. To fill the remaining \(\frac{1}{2}\), it requires:

\(\frac{1}{2} \div \frac{1}{15} = \frac{1}{2} \times 15 = 7.5\) minutes.

Therefore, the total time= 5 + 7.5= 12.5 minutes