Question

The difference between the ages of two brothers is same as the difference between the ages of the father and mother. The age of elder brother is 25 years. At the time of the birth of younger brother the mother's age was 32 years. If father's age is 5 years more than mother's age, then what was the age of father at the time of elder brother's birth?

• A. 55 years
• B. 32 years
• C. 30 years
• D. 57 years

Hint:

In age-related problems, carefully define variables and use relationships between ages and differences to form equations before solving.

Answer 1

The Correct Option is B

Let's denote the ages as follows:
- Elder brother's current age = 25 years
- Mother's age at younger brother's birth = 32 years
- Father's age is 5 years more than mother's current age
- Let the age difference between the two brothers = \(d\)
- The difference between father and mother’s current age = 5 years
Step 1: Since the difference between brothers' ages is the same as the difference between father and mother’s ages, the age difference \(d = 5\) years.
Step 2: The younger brother's age = elder brother's age - difference = \(25 - 5 = 20\) years.
Step 3: Mother’s current age = mother’s age at younger brother’s birth + younger brother’s age = \(32 + 20 = 52\) years.
Step 4: Father’s current age = mother’s current age + 5 = \(52 + 5 = 57\) years.
Step 5: To find father's age at elder brother's birth, subtract elder brother's age from father's current age:
\(57 - 25 = 32\) years.
Therefore, the father was 32 years old at the time of elder brother’s birth.
Hence, the correct answer is option (B) 32 years.