The problem given in the image states:

• Ram's father was three times as old as Ram 2 years ago.
• Five years from now, his father's age will be 6 years more than twice Ram's age.

We need to determine Ram's present age.

Let:

• $x$ be Ram's current age.
• $y$ be Ram's father's current age.

Step 1: Set up equations based on the problem

Condition 1 (2 years ago):

Two years ago, Ram's father was three times Ram's age: $y - 2 = 3(x - 2)$ Simplifying this: $y - 2 = 3x - 6$ $y = 3x - 4 \quad \text{(Equation 1)}$

Condition 2 (5 years from now):

Five years from now, Ram's father will be 6 years more than twice Ram's age: $y + 5 = 2(x + 5) + 6$ Simplifying this: $y + 5 = 2x + 10 + 6$ $y + 5 = 2x + 16$ $y = 2x + 11 \quad \text{(Equation 2)}$

Step 2: Solve the system of equations

Now, we have two equations:

1. $y = 3x - 4$
2. $y = 2x + 11$

Equating these two expressions for $y$: $3x - 4 = 2x + 11$ Solve for $x$: $3x - 2x = 11 + 4$ $x = 15$

Step 3: Find Ram's father's age

Using Equation 1: $y = 3(15) - 4 = 45 - 4 = 41$

Conclusion:

Ram's current age is 15 years, and his father's current age is 41 years.

Would you like more details on this, or do you have any other questions?

Here are some related questions you could explore:

1. How would the solution change if the conditions on ages were different?
2. Can you solve this problem graphically using lines?
3. What would happen if the father's age was twice Ram's age 2 years ago?
4. How do age-related word problems typically fit into algebraic systems?
5. How can you verify the solution by plugging it back into the original conditions?

Tip: In age-related word problems, always write down each condition clearly as an equation before solving the system.