The present ages of Trisha and Shalini are in the ratio of `7 : 6` respectively. After 8 years the ratio of their ages will be `9 : 8`. What is the difference in their ages?

Options

A. 4 years
B. 8 years
C. 10 years
D. 12 years

Explanation

To solve the problem, we will follow these steps:

1. **Define the Present Ages**:
Let Trisha's present age be \( 7x \) and Shalini's present age be \( 6x \), where \( x \) is a common multiplier.

2. **Set Up the Future Age Equation**:
After 8 years, Trisha's age will be \( 7x + 8 \) and Shalini's age will be \( 6x + 8 \). According to the problem, the ratio of their ages after 8 years will be \( 9:8 \). Therefore, we can set up the equation:
\[ \frac{7x + 8}{6x + 8} = \frac{9}{8} \]

3. **Cross Multiply to Eliminate the Fraction**:
Cross multiplying gives us:
\[ 8(7x + 8) = 9(6x + 8) \]

4. **Expand Both Sides**:
Expanding both sides results in:
\[ 56x + 64 = 54x + 72 \]

5. **Rearrange the Equation**:
To isolate \( x \), we will move all terms involving \( x \) to one side and constant terms to the other:
\[ 56x - 54x = 72 - 64 \]
This simplifies to:
\[ 2x = 8 \]

6. **Solve for \( x \)**:
Dividing both sides by 2 gives:
\[ x = 4 \]

7. **Calculate the Present Ages**:
Now, we can find the present ages of Trisha and Shalini:
- Trisha's age: \( 7x = 7 \times 4 = 28 \) years
- Shalini's age: \( 6x = 6 \times 4 = 24 \) years

8. **Find the Difference in Their Ages**:
The difference in their ages is:
\[ 28 - 24 = 4 \text{ years} \]

Thus, the difference in their ages is **4 years**.