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Question 14 : A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is :

1. 9.5
2. 10
3. 4.5
4. 6

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Method of solving this CAT Question from Mixtures and Alligations

Let the average marks scored by boys during the mid semester exam be n.
Then, the girls’ average mark will be n + 5.
On calculation, the average of the entire class will be n + 3.
This is in the ratio of 2 : 3 since there are 20 boys and 30 girls in the class.

During the final exam, the average score of the girls dropped by 3.
So, n + 5 becomes n + 2 while the average score of the entire class increased by 2 or it becomes n + 5.
Using alligation we can say that the difference between the average mark of entire class and average mark of girls is 3 which is $$frac{2}{5}$th of the total. Hence $\frac{3}{5}$th of the total is 4.5. Thus the average of boys =$n + x) – (n + 5) = 4.5,
On solving we get x = 9.5.

The question is "A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is :"

Choice A is the correct answer.

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