If `a :b::3:4 & b:c:: 4:7.` then `(a +b + c)/( c ) = ?`

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem, we need to find the value of \((a + b + c) / c\) given the ratios \(a : b = 3 : 4\) and \(b : c = 4 : 7\).

### Step-by-Step Solution:

1. **Understanding the Ratios**:
- From the ratio \(a : b = 3 : 4\), we can express \(a\) and \(b\) in terms of a common variable \(k\):
\[ a = 3k \quad \text{and} \quad b = 4k \]

2. **Expressing \(c\) in terms of \(k\)**:
- From the ratio \(b : c = 4 : 7\), we can express \(b\) and \(c\) in terms of another common variable \(m\):
\[ b = 4m \quad \text{and} \quad c = 7m \]
- Since \(b\) is the same in both ratios, we can set \(4k = 4m\). This implies that \(k = m\).

3. **Finding \(c\)**:
- Now substituting \(k\) for \(m\) in the expression for \(c\):
\[ c = 7m = 7k \]

4. **Calculating \(a + b + c\)**:
- Now we can express \(a + b + c\) in terms of \(k\):
\[ a + b + c = 3k + 4k + 7k = 14k \]

5. **Finding \((a + b + c) / c\)**:
- Now we can substitute \(c\) into the expression:
\[ \frac{a + b + c}{c} = \frac{14k}{7k} \]
- Simplifying this gives:
\[ \frac{14k}{7k} = 2 \]

### Final Answer:
Thus, the value of \((a + b + c) / c\) is \(2\).