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

###### CAT Questions | Ratio and Proportion | Mixtures

The question is from CAT Ratio, Mixtures and Averages. It is about two mixtures. What is the percentage of one variable when two mixtures are clubbed together? 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 2020.

Question 12: Class A has boys to girls in the ratio 2 : 3, Class B has girls to boys in the ratio 5 : 3. If the number of students in Class A is at least twice as many as the number of students in Class B, what is the minimum percentage of boys when both classes are considered together?

1. 33.33%
2. 40%
3. 39.17%
4. 37.5%

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##### 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.

Let us first rewrite the numbers a touch – 40% of students in Class A are boys, and 37.5% of boys in class B are boys. The overall percentage of boys should lie between these two numbers.

Now, class A has at least twice as many students as class B. So, the overall weighted average should definitely be closer to the percentage of boys in class A, or closer to 40%.

Now, the number of students in class A can be much higher than the number in class B, in which case the overall percentage would practically be 40%, This is the maximum percentage that can be there.

For the minimum percentage, we need to consider the other extreme-where class A has exactly twice as many students as class B.
The weighted average would be $$frac{2 * 40 + 1 * 37.5}{3}\\$ = 39.17% The question is "what is the minimum percentage of boys when both classes are considered together?" ##### Hence, the answer is "39.17%". Choice C is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in ChennaiPrices slashed by Rs 4000/- Attend a Demo Class ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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