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in Commercial Mathematics by (49.1k points)
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A tap can fill a bath in 20 minutes and another tap can fill it in 30 minutes. Amit opens both the taps simultaneously. When the both should have been full, he finds that the waste pipe was open. He then closes the waste pipe and in another 4 minutes the bath is full. In what time would the waste pipe empty it?

(a) 35 min

(b) 38 min

(c) 36 min

(d) 39 min

1 Answer

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by (48.0k points)
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Best answer

Correct option is (c) 36 min

A work done in 1 minute by both the taps = \(\left(\frac 1{20} + \frac 1{30}\right) \)

\(= \frac 5{60} \)

\(= \frac 1{12}\)

Both the taps can fill the bath in 12 minutes. Clearly the waste pipe empties as much the bath in 12 minutes as the other two two taps together can fill in 4 minutes.

Work done by two taps in 4 minutes = \(\frac 1{12} \times 4 = \frac 13\)

In 12 minutes, the waste pipe empties = \(\frac 13 \) part

In 1 minute, the waste pipe empties = \(\frac 13 \times \frac 1{12} = \frac 1{36}\) part

Thus the waste pipe can empty the bath in 36 minutes.

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