Age Ratio Calculation

Let the present ages of Sheo Kumar and Dileep Kumar be $9x$ and $10x$ respectively, according to the given ratio $9 : 10$.

Future Age Projection

After $11\text{ years}$, their ages will be:

• Sheo Kumar's age: $(9x + 11)$ years
• Dileep Kumar's age: $(10x + 11)$ years

Setting Up the Equation

The problem states that after $11\text{ years}$, the ratio of their ages will be $10 : 11$. We can write this as an equation:

Solving for x

Cross-multiply to solve for $x$:

$11(9x + 11) = 10(10x + 11)$

$99x + 121 = 100x + 110$

Rearrange the terms to find $x$:

$121 - 110 = 100x - 99x$

$11 = x$

Determining Present Ages

Now, substitute the value of $x=11$ back into the expressions for their present ages:

• Sheo Kumar's present age = $9x = 9 \times 11 = 99\text{ years}$
• Dileep Kumar's present age = $10x = 10 \times 11 = 110\text{ years}$

Therefore, the present ages are $99\text{ years}$ and $110\text{ years}$.