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.