The difference between the ages of the two brothers is half the difference between the ages of their parents. The elder brother is 18 years of age. Their father's age was 32 years when the younger brother was born who is now 15 years old. What is their mother's age?

Younger brother is 15, father was 32 when younger was born, so father is now 32 + 15 = 47. Elder brother is 18, so brothers' age difference = 18 - 15 = 3 years. Half of parents' age difference = 3, so parents' age difference = 6 years. Let mother's age = m, father's age = 47. We need m - 47 = ±6 (we don't know who's older). If father is 6 years older: m = 47 - 6 = 41. Option B (41) fits. If mother is 6 years older: m = 47 + 6 = 53 (not an option). So mother is 41. Option B is correct.