Two taps can fill an empty cistern in 8 min and 20 min , respectively. However, together, they take 30 min to fill it because of a leak. How much time will the leak take to empty a full cistern?

Correct option is A

​$$\frac{1}{8} + \frac{1}{20} - \frac{1}{x} = \frac{1}{30}\\\Rightarrow \frac{1}{x} = \frac{1}{8} + \frac{1}{20} - \frac{1}{30}\\\Rightarrow \frac{1}{x} = \frac{15 + 6 - 4}{120}\\\Rightarrow \frac{1}{x} = \frac{17}{120}\\\Rightarrow x = \frac{120}{17}$$​​