Question

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 bath 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

Answer 1

The correct option is C $36$ min

A work done in $1$ minute by both the taps $=(\frac{1}{20}+\frac{1}{30})=\frac{5}{60}=\frac{1}{12}$

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 $=\frac{1}{12}\times 4=\frac{1}{3}$.

In $12$ minutes, the waste pipe empties $=\frac{1}{3}$ part.

In $1$ minute, the waste pipe empties $=\frac{1}{3}\times \frac{1}{12}=\frac{1}{36}$ part.

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