Correct Answer - Option 4 : 3
Let the sum of ages of the members of the family initially be ‘x’ years and the age of the child when counted after 5 years be ‘y’ years
After 5 years, sum of the 7 members of the family = x + 7 × 5 (∵ Each person’s age increase by 5)
Sum of ages of the member = x + 35 + y
⇒ x/(x + 35 + y) = 105/ 124
⇒ 124x = 105x + 3675 + 105y
⇒ 19x – 105y = 3675 ---- 1
Sum of the ages of the members after 9 years = x + 35 + y + 4 × 8 (∵ 4 more years and 8 members are there)
⇒ x + y + 67
⇒ x/(x + y + 67) = 3/4
⇒ 4x = 3x + 3y + 201
⇒ x – 3y = 201 ---- 2
Equation 1 – 35 × Equation 2
⇒ 19x – 35x = 3675 – 35 × 201
⇒ -16x = -3360
∴ x = 210
Substituting in equation 2
⇒ 210 – 3y = 201
⇒ y = 3
∴ The age of the child when counted after 5 years was 3 years.