Question

In a family consisting of four living generations (excluding married daughters), the wife is always three years younger than her husband. The siblings in the family have an age gap of three years and there are 2 siblings in the youngest generation. Each father is thirty years older than his eldest child. The present age of the youngest daughter is six years and her father has no siblings. Based on this information, what is the age difference between the youngest child and her grandmother?

• A. 69 years
• B. 60 years
• C. 57 years
• D. 63 years

Hint:

When solving generational age problems, work step-by-step from the youngest known age and use relative age gaps and relationships.

Answer 1

The Correct Option is B

Step 1: Identify the four generations.
Let’s denote the youngest daughter as Generation 1 (age 6). Her elder sibling (also Generation 1) would be \(6 + 3 = 9\) years old (due to a 3-year gap). Step 2: Find the father’s age (Generation 2).
According to the problem, a father is 30 years older than his eldest child. So, the father is: \[ 9 + 30 = 39 \text{ years} \] Step 3: Find the mother’s age.
She is 3 years younger than her husband: \[ 39 - 3 = 36 \text{ years} \] Step 4: Find the grandfather’s age (Generation 3).
Father’s father is 30 years older than him: \[ 39 + 30 = 69 \text{ years} \] Step 5: Find the grandmother’s age.
She is 3 years younger than her husband: \[ 69 - 3 = 66 \text{ years} \] Step 6: Compute the difference between the youngest daughter (6) and the grandmother (66): \[ 66 - 6 = 60 \text{ years} \]