Hari’s family consisted of his younger brother (Chari), younger sister (Gouri)

Linear Equations

Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.

  1. 5 years
  2. 6 years
  3. 7 years
  4. 8 years
  5. 9 years

Answer

The family has 5 members. First Hari was born, then Chari was born, and then Gauri was born.

At Gauri's birth, let ages be F (father), M (mother), H (Hari), Chari (C) and G (Gauri).

So, G = 0 (Birth of Gauri)

1. Chari is 4 years older than Gouri.

C = G + 4 = 4 (Chari was born 4 years earlier)

2. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years.

(H-4) + (F-4) + (M-4) = 70

H + F + M = 82

3. At the time of Gouri’s birth, the sum of the ages of four family members was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth.

F + M + H + C = 2(F-H + M-H)

82 + 4 = 2(82 - H - 2H)

43 = 82 - 3H

3H = 82 - 43 = 39

H = 13

So, H - C = 13 - 4 = 9

The correct option is E.