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Let's solve the problem step by step.

The given information is:

- The ratio of the present age of the father to the son is 7:2.
- After 10 years, the ratio of their ages will be 9:4.
  
Let the present age of the father be \( 7x \) and the present age of the son be \( 2x \).

After 10 years:

- Father's age will be \( 7x + 10 \)
- Son's age will be \( 2x + 10 \)

According to the problem, after 10 years, the ratio of their ages will be 9:4. Thus, we have the equation:

\[
\frac{7x + 10}{2x + 10} = \frac{9}{4}
\]

Now, we can solve this equation to find \( x \):

\[
4(7x + 10) = 9(2x + 10)
\]

Expanding both sides:

\[
28x + 40 = 18x + 90
\]

Simplifying:

\[
28x - 18x = 90 - 40
\]

\[
10x = 50
\]

\[
x = 5
\]

Now, the present age of the father is:

\[
7x = 7 \times 5 = 35
\]

Therefore, the present age of the father is **35 years**.

Let me know if you want more details or if you have any questions.

Here are 5 related questions:
1. What is the present age of the son?
2. How old will the father be in 15 years?
3. What is the difference in age between the father and the son?
4. What would their age ratio be in 5 years?
5. If the son's age was doubled, what would be their new ratio?

**Tip**: Always cross-check the final solution by substituting back into the given conditions.

The ratio of the present age of father to that of son is 7:2. After 10 years, their ages will be in the ratio of 9:4. The present ages of the father is?

Learn how to solve a typical age problem where the ratio of the present age of a father to his son is 7:2, and after 10 years, the ratio changes to 9:4. This problem involves algebraic manipulation and understanding ratios, perfect for students in Grades 8-10.

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