Ramesh's father's present age is three times Ramesh's age.After 12 years ,his father's age will be twice his age.find theri present age.

Let's denote:

- Ramesh's present age as \( R \) years.
- His father's present age as \( F \) years.

### Step 1: Set up the equations based on the given conditions.

1. **First condition:** Ramesh's father's present age is three times Ramesh's age.
   \[
   F = 3R
   \]

2. **Second condition:** After 12 years, his father's age will be twice Ramesh's age.
   \[
   F + 12 = 2(R + 12)
   \]

### Step 2: Solve the system of equations.

#### Substituting \( F = 3R \) from the first equation into the second equation:
\[
3R + 12 = 2(R + 12)
\]
Now, expand the right-hand side:
\[
3R + 12 = 2R + 24
\]
Subtract \( 2R \) from both sides:
\[
R + 12 = 24
\]
Subtract 12 from both sides:
\[
R = 12
\]

### Step 3: Find the father's present age.

Since \( F = 3R \) and \( R = 12 \):
\[
F = 3 \times 12 = 36
\]

### Final Answer:
- Ramesh's present age is 12 years.
- His father's present age is 36 years.

Would you like more details or have any questions about this solution?

Here are 5 related questions:
1. What will be the sum of their ages after 10 years?
2. If Ramesh's father's age was twice his age 5 years ago, what would their current ages be?
3. How would the equation change if his father's age was 4 times Ramesh's current age?
4. How old was Ramesh when his father was 24 years old?
5. What would their ages be if the conditions were reversed (Ramesh’s age being three times his father’s)?

**Tip:** Setting up clear equations based on the conditions is key to solving age-related problems.

Ramesh's father's present age is three times Ramesh's age. After 12 years, his father's age will be twice his age. Find their present ages.

This problem involves solving a classic age-related question using linear equations. Learn how to find Ramesh's and his father's current ages when given that the father's age is three times Ramesh's age, and in 12 years, the father's age will be twice Ramesh's age. Suitable for students in Grades 6-8.

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