Two pipes A and B can fill a cistern in 10 minutes and 15 minutes respectively. Both pipes are opened together. The cistern will be filled in just 8minutes, if the pipe B is turned off after:a)2 minutesb)4 minutesc)3 minutesd)5 minutesCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Pipes A and B filling a cistern in different time intervals:

Let's first calculate the individual rates at which pipes A and B fill the cistern.

- Pipe A fills the cistern in 10 minutes, so its filling rate is 1/10 of the cistern per minute.
- Pipe B fills the cistern in 15 minutes, so its filling rate is 1/15 of the cistern per minute.

Working together:

When both pipes are opened together, their rates of filling are additive. So, the combined filling rate of pipes A and B is:

1/10 + 1/15 = 3/30 + 2/30 = 5/30 of the cistern per minute.

This means that together, pipes A and B fill 5/30 or 1/6 of the cistern per minute.

Finding the time:

To find the time it takes to fill the cistern when pipe B is turned off after a certain amount of time, we can set up the following equation:

(1/10 + 1/15) * t = 1

where 't' represents the time in minutes.

Calculating the time when pipe B is turned off after 3 minutes:

By substituting 't' with 3 in the equation, we get:

(1/10 + 1/15) * 3 = 1

Simplifying further:

(3/30 + 2/30) * 3 = 1

(5/30) * 3 = 1

5/10 = 1

1 = 1

Explanation:

From the equation, we can see that when pipe B is turned off after 3 minutes, the cistern will be filled in 8 minutes. This means that pipe A alone is capable of filling the remaining 5/6 of the cistern in 5 minutes.

Therefore, the correct answer is option 'C' - 3 minutes.

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