The present ages of Vikas and Sujit are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Sujit's present age in years?

Options

A. 6
B. 24
C. 18
D. 27

Explanation

To solve the problem, we will follow these steps:

1. **Define the Present Ages**: Let the present age of Vikas be \( 5x \) and the present age of Sujit be \( 4x \), where \( x \) is a common multiplier.

2. **Set Up the Future Age Equation**: In three years, Vikas's age will be \( 5x + 3 \) and Sujit's age will be \( 4x + 3 \).

3. **Establish the Ratio in Three Years**: According to the problem, the ratio of their ages in three years will be \( 11:9 \). Therefore, we can set up the equation:
\[ \frac{5x + 3}{4x + 3} = \frac{11}{9} \]

4. **Cross Multiply to Eliminate the Fraction**: Cross multiplying gives us:
\[ 9(5x + 3) = 11(4x + 3) \]

5. **Expand Both Sides**: Expanding both sides, we have:
\[ 45x + 27 = 44x + 33 \]

6. **Rearrange the Equation**: Rearranging gives:
\[ 45x - 44x = 33 - 27 \]
\[ x = 6 \]

7. **Calculate Sujit's Present Age**: Now we can find Sujit's present age:
\[ \text{Sujit's age} = 4x = 4 \times 6 = 24 \]

Thus, Sujit's present age is **24 years**.