# CAT Practice : Averages, Ratios, Mixtures

Based on the sum of ages of the couple and the children, we first need to find the time gap between the birth of each child!

## Age of the twin children

Q.22: The average age of a couple was 24 years. After their 1st and 2nd children (twins) were born, the average age of the family became 13.5 years. The average age of the family just after 3rd child was born was 13.2 years. The average age of the family after 4th child was born was 16 years. The current average age of the family is 19 years. What is the current age of the twin children?
1. 14 years
2. 15 years
3. 11 years
4. 12 years

Choice D. 12 years

## Detailed Solution

Sum of the ages of the couple = 24 * 2 = 48
After the 1st and 2nd children, sum = 13.5 * 4 = 54
Difference in sum = 54 – 48 = 6 years
Or after 6/ 2 = 3 years, the twin were born to the couple (Ages of children at the time of birth is 0)

After 3rd child, sum = 13.2 * 5 = 66 yrs

Difference = 66 – 54 = 12
Or after 12/4 = 3 yrs, 3rd child was born (Couple + 2 children were already present. So 4)

After 4th child, sum = 16 * 6 = 96 yrs
Difference = 96 – 66 = 30
Or after 30/5 = 6 yrs, 4th child was born

Current sum = 19 * 6 = 114 yrs
Difference 114 – 96 = 18 yrs
Or after 18/6 = 3 yrs

The gap between the children are as follows: 3 yrs, 6 yrs and 3 yrs
Age of eldest ones = 3 + 6 + 3 = 12

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