Institution: AGRANI BANK LTD Exam: Agrani bank Ltd - Officer - 12.02.2010
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To determine what part of the staff earns below Tk. 15,000, we can start by analyzing the information step by step.

Let’s assume the total number of employees in the company is represented by \( T \). According to the question, one-half of the employees earn over Tk. 18,000. Therefore, the number of employees earning over Tk. 18,000 is \( \frac{T}{2} \).

The remainder of the employees is thus \( T - \frac{T}{2} = \frac{T}{2} \).

Next, we have one-third of this remainder earning between Tk. 15,000 and Tk. 18,000. This number amounts to:

\[
\frac{1}{3} \times \frac{T}{2} = \frac{T}{6}
\]

Now, we analyze the earnings below Tk. 15,000. The remaining number of employees who earn below Tk. 15,000 can be calculated by subtracting the employees earning between Tk. 15,000 and Tk. 18,000 from the remainder:

\[
\frac{T}{2} - \frac{T}{6}
\]

Finding a common denominator (which is 6) gives:

\[
\frac{3T}{6} - \frac{T}{6} = \frac{2T}{6} = \frac{T}{3}
\]

Now, to find the proportion of the total staff that earns below Tk. 15,000, we compare this number to the total:

\[
\text{Proportion below } Tk. 15,000 = \frac{\frac{T}{3}}{T} = \frac{1}{3}
\]

Thus, one-third of the staff earns below Tk. 15,000, confirming that the correct answer is **C) one-third**.