# CAT Practice : Averages, Ratios, Mixtures

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.

## Mixture of two mixtures

Q.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%

Choice C. 39.17%

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## Detailed Solution

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

2 x 40% + 1 x 37.5% / 3
= 39.17%

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