Institution: SONALI BANK LTD Exam: Sonali Bank Ltd - Assistant Engineer (IT) - 26.08.2016 ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

Let's denote the total number of faculty members as \( x \). According to the problem, one-third of the faculty members are female, which means the number of female faculty members is \( \frac{x}{3} \). Consequently, the number of male faculty members would be \( x - \frac{x}{3} = \frac{2x}{3} \).

We know that 16 male faculty members are unmarried, and 60% of the male faculty members are married. Let’s set up the equation based on the information about married males. If 60% of the males are married, that means 40% are unmarried. Therefore, we can express the number of unmarried males as:

\[
0.4 \times \frac{2x}{3} = 16
\]

To solve for \( x \), we multiply both sides by 100 to eliminate the decimal:

\[
\frac{2x}{3} = 16 \div 0.4
\]

Calculating the right side:

\[
16 \div 0.4 = 16 \times \frac{10}{4} = 16 \times 2.5 = 40
\]

Now we equate it back to the equation:

\[
\frac{2x}{3} = 40
\]

Multiplying both sides by 3 gives:

\[
2x = 120
\]

Finally dividing by 2 yields:

\[
x = 60
\]

Thus, the total number of faculty members in the department is **60**, which corresponds to option B.