The difference between the ages of two brothers is 8 years when father’s age is 54. Father is elder by two years to mother. Younger brother’s age is half of mother’s age. Find the age of elder brother.

Let younger brother = y, elder brother = e (e = y + 8). Mother = 2y (younger is half of mother). Father = 54, mother = 52 (father is 2 years older). So 2y = 52, y = 26. Younger brother is 26, so elder brother = 26 + 8 = 34. All conditions are satisfied: difference is 8, father-mother age difference is 2, and younger is half of mother's age.