A tap can fill a tank in $$5\frac{1}{2}$$ hours. Because of a leak, it took $$8\frac{1}{4}$$ hours to fill the tank. In how much time (in hours) will the leak alone empty 30% of the tank?

$$\eqalign{ & {\text{I fill the tank}} = 5\frac{1}{2} = \frac{{11}}{2}{\text{ in hour}} \cr & {\text{I - II fill the tank}} = 8\frac{1}{4} = \frac{{33}}{4}{\text{ in hour}} \cr & {\text{LCM }}\left( {11,\,33} \right) = 33 \cr} $$

$$\eqalign{ & {\text{Total work }}30\% = 33 \times \frac{{30}}{{100}} = \frac{{99}}{{10}} \cr & {\text{II}} = {\text{leak pipe efficiency}} = 6 - 4 = 2 \cr} $$
Time taken by pipe to empty the tank = $$\frac{{99}}{{\frac{{10}}{2}}}$$ = $$\frac{{99}}{{20}}$$ in hour