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A family consists of 7 members. Within next 5 years, the total number of members rose to 8 because a baby was born (sometime in that 5 years). The ratio of total age of the family members initially and 5 years after was found to be 105 ∶ 124. After 9 years (from initial time), the ratio of age initially and 9 years after was found to be 3 ∶ 4. What was the age of the child when counted after 5 years? (in years)

A family consists of 7 members. Within next 5 years, the total number of members rose to 8 because a baby was born (sometime in that 5 years). The ratio of total age of the family members initially and 5 years after was found to be 105 ∶ 124. After 9 years (from initial time), the ratio of age initially and 9 years after was found to be 3 ∶ 4. What was the age of the child when counted after 5 years? (in years) Correct Answer 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.

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