Sahil is younger than Ranjeet by 8 years. If their ages are in the respective ratio of 7:9, then what is the age of Sahil ?

Options

A. 16 years
B. 18 years
C. 28 years
D. 14 years

Answer

To solve the problem step by step, we can follow these instructions:

1. **Define Variables**:
Let Sahil's age be represented as \( S \) and Ranjeet's age as \( R \).

2. **Set Up the Relationship**:
According to the problem, Sahil is younger than Ranjeet by 8 years. This can be expressed as:
\[ R = S + 8 \]

3. **Set Up the Ratio**:
The problem states that the ratio of their ages is 7:9. This can be written as:
\[ \frac{S}{R} = \frac{7}{9} \]

4. **Substitute R in the Ratio**:
We can substitute \( R \) from step 2 into the ratio equation:
\[ \frac{S}{S + 8} = \frac{7}{9} \]

5. **Cross-Multiply to Eliminate the Fraction**:
Cross-multiplying gives us:
\[ 9S = 7(S + 8) \]

6. **Distribute and Simplify**:
Expanding the right side:
\[ 9S = 7S + 56 \]

7. **Isolate S**:
Subtract \( 7S \) from both sides:
\[ 9S - 7S = 56 \]
This simplifies to:
\[ 2S = 56 \]

8. **Solve for S**:
Divide both sides by 2:
\[ S = 28 \]

9. **Conclusion**:
Therefore, Sahil's age is \( 28 \) years.