Institution: AGRANI BANK LTD Exam: Agrani bank Ltd - Senior Officer - 12.08.2011
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, we start with the ratio \( a : b = 2 : 3 \). This means we can express \( a \) and \( b \) in terms of a variable \( k \):
- \( a = 2k \)
- \( b = 3k \)

Next, we use the second equation given: \( a + b = 4 \). Substituting the expressions for \( a \) and \( b \) gives us:
\[
2k + 3k = 4
\]
This simplifies to:
\[
5k = 4 \implies k = \frac{4}{5}
\]
Now, we can find the values of \( a \) and \( b \):
- \( a = 2k = 2 \times \frac{4}{5} = \frac{8}{5} \)
- \( b = 3k = 3 \times \frac{4}{5} = \frac{12}{5} \)

Next, we compute \( b - a \):
\[
b - a = \frac{12}{5} - \frac{8}{5} = \frac{4}{5}
\]

The problem requires us to find the value of \( (a + b) : (b - a) \). We already know \( a + b = 4 \) and \( b - a = \frac{4}{5} \).

Thus, we calculate:
\[
(a + b) : (b - a) = 4 : \frac{4}{5}
\]
To simplify this, we multiply both sides by 5:
\[
4 \times 5 : 4 = 20 : 4
\]
Dividing both sides by 4 gives:
\[
5 : 1
\]

Thus, the final answer is \( 5 : 1 \), which corresponds to option B.