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Select the correct answerA pipe can fill a bath in 15 minutes and another can fill it in 30 minutes. A person opens both the pipes simultaneously. When the bath should have been full, he finds that the waste pipe was open. He then closes the waste pipe and in 3 minutes more, the bath is full. In what time, would the waste pipe empty it?radio_button_unchecked100/3radio_button_unchecked30radio_button_unchecked40radio_button_unchecked80/3

Question

Select the correct answerA pipe can fill a bath in 15 minutes and another can fill it in 30 minutes. A person opens both the pipes simultaneously. When the bath should have been full, he finds that the waste pipe was open. He then closes the waste pipe and in 3 minutes more, the bath is full. In what time, would the waste pipe empty it?radio_button_unchecked100/3radio_button_unchecked30radio_button_unchecked40radio_button_unchecked80/3

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Solution

Let's solve this step by step:

Step 1: Find the rate at which each pipe can fill the bath.

The first pipe can fill the bath in 15 minutes, so it fills 1/15 of the bath per minute. The second pipe can fill the bath in 30 minutes, so it fills 1/30 of the bath per minute.

Step 2: Find the combined rate of the two pipes.

When both pipes are open, they fill the bath at a rate of 1/15 + 1/30 = 1/10 of the bath per minute.

Step 3: Find the rate at which the bath is actually filled.

The bath is filled in the time it should have been full plus 3 minutes. This means the bath is filled at a rate of 1/(time it should have been full + 3) of the bath per minute.

Step 4: Find the rate at which the waste pipe empties the bath.

The waste pipe's rate is the difference between the combined rate of the two pipes and the actual rate at which the bath is filled.

So, the waste pipe empties the bath at a rate of 1/10 - 1/(time it should have been full + 3) of the bath per minute.

Step 5: Solve for the time it would take the waste pipe to empty the bath.

The time it would take the waste pipe to empty the bath is the reciprocal of the rate at which it empties the bath.

So, the time it would take the waste pipe to empty the bath is 1/(1/10 - 1/(time it should have been full + 3)) minutes.

Given that the bath is full in 3 minutes more after closing the waste pipe, the time it should have been full is 10 minutes (since 1/10 of the bath is filled per minute).

So, the time it would take the waste pipe to empty the bath is 1/(1/10 - 1/(10 + 3)) = 1/(1/10 - 1/13) = 1/(3/130) = 130/3 = 40 minutes.

So, the correct answer is 40 minutes.

This problem has been solved

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