An irrigation inlet pipe can fill a farm pond in $8\text{ hours}$. However, due to seepage at the bottom of the pond, it takes $10\text{ hours}$ to fill the pond completely when the pipe is running. If the inlet pipe is closed when the pond is full, how many hours will the seepage alone take to empty the pond completely?
Options:
(A) $30\text{ hours}$
(B) $35\text{ hours}$
(C) $40\text{ hours}$
(D) $45\text{ hours}$
Answer Key:
C
Step-by-Step Solution & Explanation
**Method 1: Net Flow Rate**
Let the seepage emptying rate be $R_s$ and inlet pipe filling rate be $R_i = \frac{1}{8}\text{ pond/hr}$.
When both are active:
$R_i - R_s = \frac{1}{10}$
$R_s = \frac{1}{8} - \frac{1}{10} = \frac{5 - 4}{40} = \frac{1}{40}\text{ pond/hr}$
Thus, time taken by seepage alone to empty the pond $= \frac{1}{1/40} = 40\text{ hours}$.
Option **C** is correct.