Sourish is now 25 years old while his cousin is 7 years . After how many years will Sourish's age be 2.5 times that of his cousin ?

Options

A. 4
B. 5
C. 6
D. 3

Answer

To solve the problem, we need to determine after how many years Sourish's age will be 2.5 times that of his cousin's age.

### Step-by-Step Solution:

1. **Identify Current Ages**:
- Sourish's current age (S) = 25 years
- Cousin's current age (C) = 7 years

2. **Set Up the Equation**:
- Let the number of years after which Sourish's age will be 2.5 times his cousin's age be denoted as \( x \).
- After \( x \) years, Sourish's age will be \( 25 + x \).
- After \( x \) years, his cousin's age will be \( 7 + x \).

3. **Formulate the Equation**:
- According to the problem, we want Sourish's age to be 2.5 times his cousin's age:
\[ 25 + x = 2.5 \times (7 + x) \]

4. **Expand and Simplify the Equation**:
- Expanding the right side:
\[ 25 + x = 2.5 \times 7 + 2.5 \times x \]
\[ 25 + x = 17.5 + 2.5x \]

5. **Rearranging the Equation**:
- Move all terms involving \( x \) to one side and constant terms to the other side:
\[ 25 - 17.5 = 2.5x - x \]
\[ 7.5 = 1.5x \]

6. **Solve for \( x \)**:
- Divide both sides by 1.5:
\[ x = \frac{7.5}{1.5} = 5 \]

7. **Conclusion**:
- After 5 years, Sourish's age will be 2.5 times that of his cousin's age.

### Final Answer:
Sourish's age will be 2.5 times that of his cousin's age after **5 years**.

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