Institution: Bangladesh Bank Exam: অফিসার (ক্যাশ ) - Sonali | Rupali | BD Krishi | Rajshahi Krishi Unnayn | Investment Corporation Of Bangladesh - ২৯. ০৩.২০১৯ ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve this problem, we need to first establish the rates at which the pump fills the tank and how the leak drains it.

The pump can fill the tank in 2 hours, which means its filling rate is \( \frac{1}{2} \) of the tank per hour. Therefore, in 1 hour, the pump fills \( 0.5 \) of the tank.

When the leak is present, it takes \( 2 \frac{1}{3} \) hours (or \( \frac{7}{3} \) hours) to fill the tank. This gives us the rate at which the tank is being filled in this case, which is \( \frac{1}{\frac{7}{3}} = \frac{3}{7} \) of the tank per hour.

Now, we can determine the rate of the leak. The effective filling rate with the leak can be expressed as the filling rate of the pump minus the draining rate of the leak:

\[
\text{Filling Rate} - \text{Leak Rate} = \text{Effective Rate}
\]
\[
\frac{1}{2} - \text{Leak Rate} = \frac{3}{7}
\]

To find the leak rate, we rearrange the equation:

\[
\text{Leak Rate} = \frac{1}{2} - \frac{3}{7}
\]

To perform this subtraction, we convert \( \frac{1}{2} \) into sevenths:

\[
\frac{1}{2} = \frac{7}{14}, \quad \frac{3}{7} = \frac{6}{14}
\]

Now, subtract these fractions:

\[
\text{Leak Rate} = \frac{7}{14} - \frac{6}{14} = \frac{1}{14}
\]

This means the leak drains \( \frac{1}{14} \) of the tank per hour. Therefore, it will take 14 hours for the leak to drain the entire tank by itself, which corresponds to option B.