Institution: Bangladesh Bank Exam: Officer (General) -Ansar VDP Unnayan | BD House Building Finance Corporation 28.09.2018 ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, let's denote the three numbers as \( a \), \( b \), and \( c \).

The problem states that the average of the first and the second numbers is 15 more than the average of the second and the third numbers. We can express this mathematically as follows:

1. The average of the first and second numbers is given by:
\[
\frac{a + b}{2}
\]

2. The average of the second and third numbers is:
\[
\frac{b + c}{2}
\]

According to the problem, we have:
\[
\frac{a + b}{2} = \frac{b + c}{2} + 15
\]

We can eliminate the fractions by multiplying everything by 2, resulting in:
\[
a + b = b + c + 30
\]

Simplifying this equation by subtracting \( b \) from both sides gives:
\[
a = c + 30
\]

From this relationship, we see that the first number \( a \) is 30 units greater than the third number \( c \). To find the difference between the first number and the third number, we calculate:
\[
a - c = (c + 30) - c = 30
\]

Since 30 is not an option given in the choices (15, 45, 60, None of these), the correct answer is indeed **D: None of these**. This demonstrates the importance of careful mathematical manipulation to derive a clear understanding of relationships between the variables.