Twelve years hence, the ratio between the ages of C and E is 5:7 respectively. The present age of A is 25% less than that of D. Four years ago, the average age of B and D was 18 years. B is six years younger than E. Three years hence, the age of E is three years less than double the age of A. After 7 years, how many people’s age will be a prime number.

Solution

Twelve years hence, the ratio between the ages of C and E is 5:7 respectively. Let’s assume that twelve years hence the ages of C and E is 5z and 7z respectively. Present age of C = (5z-12) years Present age of E = (7z-12) years B is six years younger than E. Present age of B = Present age of E - 6 = (7z-12) - 6 = (7z-18) years The present age of A is 25% less than that of D. Let’s assume the present age of D is ‘4a’ years present age of A = (100-25)% of 4a = 75% of 4a = 3a Four years ago, the average age of B and D was 18 years. Present age of B + Present age of D - 4 - 4 = 18x2 (7z-18) + 4a - 8 = 36 (7z-26) + 4a = 36 7z + 4a = 62 7z = (62-4a)    Eq.(i) Three years hence, the age of E is three years less than double the age of A. (7z-12)+3 = 2x(3a+3)-3 Put Eq.(i) in the above equation. (62-4a-12)+3 = 2x(3a+3)-3 (50-4a)+3 = 6a+6-3 53-4a = 6a+3 6a+4a = 53-3 10a = 50 a = 5 Put the value of ‘a’ in Eq.(i). 7z = (62-4x5) 7z = (62-20) 7z = 42 z = 6 After 7 years, the age of A = 3a+7 = 3x5+7 = 15+7 = 22 years After 7 years, the age of B = (7z-18)+7 = (7x6-18)+7 = (42-18)+7 = 31 years After 7 years, the age of C = (5z-12)+7 = (5x6-12)+7 = (30-12)+7 = 25 years After 7 years, the age of D = 4a+7 = 4x5+7 = 20+7 = 27 years After 7 years, the age of E = (7z-12)+7 = (7x6-12)+7 = (42-12)+7 = 37 years After 7 years, two people’s (B and E) age will be a prime number.