A tap can fill a tank in 51/2 hours. Because of a leak, it took 81/4 hours to fill the tank. In how much time (in hours) will the leak alone empty 30% of the tank?

Answer: Option B

Solution

Answer: Option B

Solution:

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

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