Age Ratio Setup

Let the present age of Ramu be represented as $4x$ years and the present age of Ravi be represented as $3x$ years. This is based on the given ratio of their present ages, which is 4:3.

Age Calculation After 5 Years

In 5 years from now:

• Ramu's age will be $ (4x + 5) $ years.
• Ravi's age will be $ (3x + 5) $ years.

Setting Up the Equation

The problem states that after 5 years, the ratio of their ages will be 5:4. We can write this as an equation:

$$ \frac{4x + 5}{3x + 5} = \frac{5}{4} $$

Solving for x

To find the value of $x$, we cross-multiply:

$$ 4(4x + 5) = 5(3x + 5) $$

Distribute the numbers:

$$ 16x + 20 = 15x + 25 $$

Now, rearrange the equation to solve for $x$. Subtract $15x$ from both sides:

$$ 16x - 15x + 20 = 25 $$

$$ x + 20 = 25 $$

Subtract 20 from both sides:

$$ x = 25 - 20 $$

$$ x = 5 $$

Calculating Present Ages

Now that we have the value of $x$, we can find their present ages:

• Ramu's present age = $ 4x = 4 \times 5 = 20 $ years.
• Ravi's present age = $ 3x = 3 \times 5 = 15 $ years.

Verification

Let's check if the ages satisfy the condition after 5 years:

• Ramu's age in 5 years = $ 20 + 5 = 25 $ years.
• Ravi's age in 5 years = $ 15 + 5 = 20 $ years.
• The ratio of their ages after 5 years is $ 25:20 $, which simplifies to $ 5:4 $. This matches the information given in the question.

Therefore, the present ages of Ramu and Ravi are 20 years and 15 years, respectively.