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

The question is from CAT Ratio, Mixtures and Averages. Milk is being diluted by adding water, we need to find out the ratio of milk to water in the diluted milk. 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 26: 3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?

1. \\frac{2187}{100}\\)
2. \\frac{81}{19}\\)
3. \\frac{729}{271}\\)
4. \\frac{743}{229}\\)

Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: When we mix two mixtures in a particular ratio, we get a third mixture. Given the third mixture how does one find the ratio in which they were mixed.

Formulae (derived using allegation):
Milk left = Capacity * (1 – fraction of milk withdrawn)ⁿ
Therefore, milk left = 30 * 0.9³
=> 30 * \\frac{9}{10}\\) * \\frac{9}{10}\\) * \\frac{9}{10}\\)
=> \\frac{2187}{100}\\)
So, Water in container = 30 – \\frac{2187}{100}\\)
=> \\frac{(3000 - 2187)}{100}\\)
=> \\frac{813}{100}\\)
Therefore, Milk : Water = 2187 : 813 = 729 : 271

The question is "What is the ratio of milk to water at the end?"

Hence, the answer is "\\frac{729}{271}\\)".

Choice C is the correct answer.