CAT Quantitative Aptitude Questions | CAT Ratios, Mixtures, Alligations and Averages Questions

The question is from CAT Ratio, Mixtures and Averages. How average age is affected when a child is born? CAT exam is known to test on basics rather than high funda ideas. A range of CAT questions can be asked from Ratios and Proportions, Mixtures, Alligations and Averages. Make sure you master the topics. 2IIMs CAT questions bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023.

Question 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

Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: 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!

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 \\frac{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 \\frac{12}{4}\\) = 3 yrs, 3^rd 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 \\frac{30}{5}\\) = 6 yrs, 4^th child was born
Current sum = 19 * 6 = 114 yrs
Difference 114 – 96 = 18 yrs
Or after \\frac{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

The question is "What is the current age of the twin children?"

Hence, the answer is "12 years".

Choice D is the correct answer.