The ratio of the ages of father and son at present is 6: 1. After 5 years the ratio will become 7:2 The present age of son is-

Options

A. 5 years
B. 6 years
C. 9 years
D. 10 years

Answer

To find the present age of the son, we can set up the problem using the information given in the question.

1. **Define Variables:**
Let the present age of the son be \( x \).
Since the ratio of the ages of the father and son is 6:1, the present age of the father will be \( 6x \).

2. **Set Up the Equation for Future Ages:**
After 5 years, the age of the son will be \( x + 5 \) and the age of the father will be \( 6x + 5 \).
According to the problem, the ratio of their ages after 5 years will be 7:2. Therefore, we can set up the equation:
\[ \frac{6x + 5}{x + 5} = \frac{7}{2} \]

3. **Cross Multiply:**
To eliminate the fraction, we can cross multiply:
\[ 2(6x + 5) = 7(x + 5) \]

4. **Expand Both Sides:**
Expanding both sides gives us:
\[ 12x + 10 = 7x + 35 \]

5. **Rearrange the Equation:**
Now, we can rearrange the equation to isolate \( x \):
\[ 12x - 7x = 35 - 10 \]
\[ 5x = 25 \]

6. **Solve for \( x \):**
Dividing both sides by 5 gives:
\[ x = 5 \]

7. **Conclusion:**
The present age of the son is \( 5 \) years.