Discussion

Question:

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.

Explanation:

Let the ages of Father and Mother at the time of Hari’s birth are F and M respectively.

Let Chari be born x years after Hari’s birth.
∴ Ages of Hari, Father and mother will be x , F + x and M + x at the time of Chari’s birth.
∴ x + (F + x) + (M + x) = 70
⇒ 3x + F + M = 70 … (1)

Gouri was born 4 years after Chari’s birth.
∴ Ages of Chari, Hari, Father and mother will be 4, 4 + x , F + x + 4 and M + x + 4 at the time of Gouri’s birth.
∴ (x + 4) + (F + x + 4) + (M + x + 4) + 4 = 2(F + M)
⇒ 3x + 16 = F + M … (2)

From (1) and (2), x = 9
Hence, option (e).

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