Statement Analysis

The question asks to find the birth year of Mr. Rajesh. We need to check the sufficiency of the given statements.

Statement 1 Analysis

Statement 1 says: "At present Mr. Rajesh is 25 years younger to his father."

Let R be Mr. Rajesh's current age and F be his father's current age.

This can be represented as: $R = F - 25$.

This statement provides only a relative age difference and does not give any absolute age or year. Therefore, Statement 1 alone is insufficient.

Statement 2 Analysis

Statement 2 says: "Mr. Rajesh’s sister who was born on 1974 is 35 years younger to his father."

Let S be the sister's current age, F be the father's current age, and Y be the current year.

The sister's age is $S = Y - 1974$.

The statement implies: $S = F - 35$.

Substituting the sister's age: $Y - 1974 = F - 35$.

This allows us to find the father's age in terms of the current year: $F = Y - 1974 + 35$, which simplifies to $F = Y - 1939$.

This statement relates the father's age to the current year using the sister's birth year but does not mention Mr. Rajesh. Therefore, Statement 2 alone is insufficient.

Combined Statements Analysis

Now, let's use both statements together.

• From Statement 1: $R = F - 25$.
• From Statement 2, we derived: $F = Y - 1939$.

Substitute the expression for F from Statement 2 into Statement 1:

$R = (Y - 1939) - 25$

$R = Y - 1964$

Mr. Rajesh's current age (R) is also defined as the current year (Y) minus his birth year: $R = Y - \text{Birth Year}$.

Equating the two expressions for R:

$Y - \text{Birth Year} = Y - 1964$

Solving for the birth year, we get: $\text{Birth Year} = 1964$.

Since we can determine a specific birth year using both statements combined, they are sufficient.

Conclusion

Statement 1 alone is insufficient. Statement 2 alone is insufficient. Both statements together are sufficient to determine Mr. Rajesh's birth year.