Age: 8 years ago, the ratio of the ages of a brother and his sister was 2:1. The sum of their present ages is 52 years. Find the brother’s present age.

Let the brother's current age be B and the sister's be S. Given: B + S = 52 → so S = 52 – B

Eight years ago: Brother’s age = B – 8 Sister’s age = S – 8 = 44 – B Ratio: (B – 8)/(44 – B) = 2/1

Cross-multiply: B – 8 = 2(44 – B) → B – 8 = 88 – 2B → 3B = 96 → B = 32

Brother’s present age is 32 years.