Question

When Ranjeev was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Ranjeev's brother is 6 years older than Ranjeev and his mother is 3 years younger than his father, how old was Ranjeev's sister when he was born?

• A. 15 years
• B. 14 years
• C. 7 years
• D. 10 years

Answer 1

Answer: (D)

10 years

Answer 2

Let Ranjeev’s age at birth be $R = 0$.
Ranjeev’s brother’s age** when Ranjeev was born:

$B = R + 6 = 0 + 6 = 6 \text{ years}$

Father’s age when Ranjeev was born:

$F = B + 32 = 6 + 32 = 38 \text{ years}$

Mother’s age when Ranjeev was born:

$M = F - 3 = 38 - 3 = 35 \text{ years}$

Sister’s age when Ranjeev was born:

$M = S + 25 \implies 35 = S + 25 \implies S = 35 - 25 = 10 \text{ years}$

Ranjeev's sister was 10 years old when he was born.