The age of my father is equal to sum of my mother’s age and my age. When I was born, the ratio of ages of my mother and father was 5 : 6. After 8 years, the ratio of my age and my mother’s age will be 3 : 8. What was my mother’s age when I was 2 years old?
Solution
Correct Answer: Option A
Let my age be M years and my mother’s age be N years.
⇒ Age of my father = (M + N) years
When I was born, the ratio of ages of my mother and father was 5 : 6.
I was born M years back.
⇒ (N - M)/(M + N - M) = 5/6
⇒ 6N - 6M = 5N
⇒ N = 6M
After 8 years, the ratio of my age and my mother’s age will be 3 : 8.
⇒ (M + 8)/(N + 8) = 3/8
⇒ 8M + 64 = 3N + 24
Put N = 6M
⇒ 8M + 40 = 18M
⇒ M = 40/10 = 4
⇒ N = 6M = 6 × 4 = 24
Mother’s age = 24 years
∴ I am 4 years old. When I was 2 years old, it would be 2 years back from now, my mother’s age was 22 years.
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