The ratio of the present ages of a and bis 6:7. After 4 years, this ratio will become 13:15. c is 8 years older to b. What is the present age (in years) of c?

Options

A. 58
B. 64
C. 60
D. 56

Answer

To solve the problem, we will follow these steps:

1. **Define Variables for Ages**:
Let the present age of A be \(6x\) and the present age of B be \(7x\), where \(x\) is a common multiplier.

2. **Set Up the Equation for Future Ages**:
In 4 years, the ages of A and B will be:
- Age of A: \(6x + 4\)
- Age of B: \(7x + 4\)

According to the problem, the ratio of their ages after 4 years will be \(13:15\). Thus, we can set up the equation:
\[ \frac{6x + 4}{7x + 4} = \frac{13}{15} \]

3. **Cross-Multiply to Solve for x**:
Cross-multiplying gives us:
\[ 15(6x + 4) = 13(7x + 4) \]
Expanding both sides:
\[ 90x + 60 = 91x + 52 \]

4. **Rearranging the Equation**:
Rearranging the equation to isolate \(x\):
\[ 90x - 91x = 52 - 60 \]
\[ -x = -8 \]
Therefore, \(x = 8\).

5. **Calculate Present Ages of A and B**:
Now we can find the present ages:
- Present age of A: \(6x = 6 \times 8 = 48\)
- Present age of B: \(7x = 7 \times 8 = 56\)

6. **Find the Present Age of C**:
Since C is 8 years older than B:
\[ \text{Present age of C} = 56 + 8 = 64 \]

Thus, the present age of C is **64 years**.