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The age of B is one-third of the sum of ages of A and C. The age of D is one-fourth of the difference of ages of E and C (C is elder than E). The age of C is six times the age of D. The age of A is 3 years and the age of C is three times the age of E. D is three years younger than B. What is the sum of ages of all persons?

The age of B is one-third of the sum of ages of A and C. The age of D is one-fourth of the difference of ages of E and C (C is elder than E). The age of C is six times the age of D. The age of A is 3 years and the age of C is three times the age of E. D is three years younger than B. What is the sum of ages of all persons? Correct Answer 26 years

Let the age of A, B, C, D, and E be A, B, C, D, and E years respectively

B = 1/3(A + C)     .....(i)

D = 1/4(C - E)     .....(ii)

C = 6D     .....(iii)

A = 3     .....(iv)

C = 3E     .....(v)

D = B – 3     .....(vi)

putting B = D + 3 in eq(i) we have

⇒ D + 3 = 1/3(3 + 6D)

⇒ D + 3 = 1 + 2D

⇒ D = 2, then C = 12(from eq iii), B = 5(from eq vi) and E = 4(from eq v)

⇒ A + B + C + D + E

⇒ 3 + 5 + 12 + 2 + 4 = 26 years

The sum of ages of all is 26 years. 

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