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

Best Answer Explained in Below-:

To solve the question of finding the ratio \( a : b : c \) given the ratios \( a : b \) and \( b : c \), we can follow these steps systematically.

We know from the problem that:

1. \( a : b = 4 : 7 \). We can express \( a \) and \( b \) in terms of a common variable \( k \):
\[
a = 4k \quad \text{and} \quad b = 7k.
\]

2. From the second ratio \( b : c = 5 : 6 \), we can express \( b \) and \( c \) in terms of another common variable \( m \):
\[
b = 5m \quad \text{and} \quad c = 6m.
\]

Since both expressions represent \( b \), we now set them equal to each other:
\[
7k = 5m.
\]

To eliminate \( k \) and \( m \), we can solve for \( m \) in terms of \( k \):
\[
m = \frac{7k}{5}.
\]

Now, we can substitute \( m \) back into the expression for \( c \):
\[
c = 6m = 6 \left( \frac{7k}{5} \right) = \frac{42k}{5}.
\]

With these expressions, we can now form the combined ratio \( a : b : c \):
\[
a = 4k, \quad b = 7k, \quad c = \frac{42k}{5}.
\]

To express them as whole numbers, we will eliminate the fraction by multiplying each term by 5:
\[
5a = 20k, \quad 5b = 35k, \quad 5c = 42k.
\]

Thus, the ratio \( a : b : c \) becomes:
\[
20 : 35 : 42.
\]

Hence, the correct answer is \( \text{B) } 20 : 35 : 42 \). This method combines understanding of equivalent ratios and algebraic manipulation to arrive at the correct ratio representation.