A father is 6 times elder to his son. After 5 years, son age will be 2/7 times of the age of his father. Find the present age of father and son.

Let's solve this problem step by step.

### Step 1: Define Variables
Let the present age of the son be \( x \) years.  
Then, the present age of the father is \( 6x \) years (since the father is 6 times older than the son).

### Step 2: Set Up the Equation
After 5 years, the son's age will be \( x + 5 \) years, and the father's age will be \( 6x + 5 \) years.

According to the problem, after 5 years, the son's age will be \( \frac{2}{7} \) of the father's age. Therefore, we can write the equation as:
\[
x + 5 = \frac{2}{7} \times (6x + 5)
\]

### Step 3: Solve the Equation
Let's solve for \( x \):

First, multiply both sides of the equation by 7 to eliminate the fraction:
\[
7(x + 5) = 2(6x + 5)
\]

Now, expand both sides:
\[
7x + 35 = 12x + 10
\]

Next, rearrange the equation to isolate \( x \):
\[
35 - 10 = 12x - 7x
\]
\[
25 = 5x
\]

Finally, solve for \( x \):
\[
x = \frac{25}{5} = 5
\]

### Step 4: Find the Present Ages
- The son's present age is \( x = 5 \) years.
- The father's present age is \( 6x = 6 \times 5 = 30 \) years.

### Final Answer
The present age of the son is **5 years**, and the present age of the father is **30 years**.

Would you like a detailed explanation of any step or have any questions?

Here are 5 related questions you might be interested in:
1. What will be their ages after 10 years?
2. If the father was 8 times older than the son, how would the equation change?
3. How do you solve similar problems involving age ratios and time shifts?
4. How can we solve for ages if the ratio is given differently?
5. Can we use algebraic methods to solve problems involving multiple people with age ratios?

**Tip:** When solving age problems, setting up clear algebraic expressions based on the given conditions is

Learn how to solve an age problem where a father is 6 times older than his son. Step-by-step solution to find the present ages of both father and son. Suitable for students in Grades 6-8.

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