A, B, C, D, are four friends. Average age of A and C is 35 years and that of B, and D is 40 years. Average age of B, C and D is 40 years. The sum of the ages of A and D is equal to that of B and C. Find out the ages (in years) of A, B, C and D.

Given :- Average age of A and C = 35 years ⇒ A + C = 70 years ......... ( ⅰ ) Average age of B, and D = 40 years. ⇒ B + D = 80 years ......... ( ⅱ ) and Average age of B, C and D = 40 years. ⇒ B + C + D = 120 years ......... ( ⅲ ) With the help of equations ( ⅰ ) , ( ⅱ ) and ( ⅲ ) , we get ∴ age of C = 40 years and age of A = 30 years According to question , ∴ age of A + age of D = age of B + age of C ⇒ A + D = B + C ⇒ 30 + D = B + 40 ⇒ D – B = 10 ∴ age of B = 35 years and age of D = 45 years