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

The question is from CAT Ratio, Mixtures and Averages. When a number is replaced by another one, average changes. How all these terms are related to each other. 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 49: Average of ‘n’ number is t. One of the numbers ‘s’ is replaced by ‘z’ and the new average becomes u. What is the relation b/w n, t, s, u and z?

1. \\frac{(u-3)}{(z-s)}\\) = \\frac{1}{n}\\)
2. \\frac{(z-s)}{u}\\) = \\frac{1}{n}\\)
3. \\frac{(t-u)}{(s-z)}\\) = \\frac{1}{n}\\)
4. \\frac{(u-3)}{(z-s)}\\) = \\frac{1}{n}\\)

Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: How the individual data points affect the average?

New Average, u = t + \\frac{(z-s)}{n}\\) (when z > s)………………..(1)
= t - \\frac{(s-z)}{n}\\) (when s < z)
= t + \\frac{(z-s)}{n}\\) (same as (1))
=> u – t = \\frac{(z-s)}{n}\\)
=> \\frac{(u – t)}{(z-s)}\\) = \\frac{1}{n}\\)
=> \\frac{(t - u)}{(s-z)}\\) = \\frac{1}{n}\\)

The question is "What is the relation b/w n, t, s, u and z?"

Hence, the answer is "\\frac{(t-u)}{(s-z)}\\) = \\frac{1}{n}\\)".

Choice C is the correct answer.