What is the birth year of Mr. Rajesh?
Statements:
1. At present Mr. Rajesh is 25 years younger to his father
2. Mr. Rajesh’s sister who was born on 1974 is 35 years younger to his father
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.
Similar Questions
- Among five people named V, W, X, Y and Z, each have a certain age. Y is four times the age of X. V is two times the age of X. Y is five times the age of W. The age of W is 12. If Z is thrice the age of V, what is the age of Z?
- Among five people named V, W, X, Y and Z, each have a certain age. The age of X is 12. V is four times the age of Z. Y is half the age of V. W is thrice the age of X. If Z is one ninth the age of W, what is the age of Y?
- 15 years ago, Shyam was twice as old as Prabhat. Five years from now Prabhat’s age will be $\frac{5}{8}$ of Shyam’s age. What is Shyam’s current age?
Important Questions from Problem on Age
The average age of a husband and his wife was 20 years at the time of their marriage. After 6 years, they have a 2 -year old child. Find the present average age of the family.
The ratio of the ages of A, B and C, 5 years ago, was 4 : 5 : 7. The sum of their present ages is 135 years. What will be the sum of the ages (in years) of B and C, 3 years from now?
The ratio of the present age of Mahesh and Ajay is 3 : 2 respectively. After 8 years. Ratio of their age will be 11: 8. What will be the present age of Mahesh’s son if his age is half of the present age of Ajay?
In a school, the average age of boys and girls together is 16.8 years, the average age of boys is 15.4 years, and the average age of girls is 18.2 years. The ratio of number of boys to girls in the school is:
The difference between age of Sunita and Sheela is 12 years. If 9 years ago, elder's age was 4 times of younger's age, then what are their present age?
A. 11 and 23
B. 15 and 27
C. 13 and 25
D. 23 and 35
