CAT Quantitative Ability Questions | CAT Averages, Ratio & Proportion questions
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CAT/2017.1
Question . 57
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:
Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Averages, Ratio & Proportion question
option A is correct
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 2525th of the total.
Hence 3535th of the total is 4.5.
Thus the average of boys = (n + x) – (n + 5) = 4.5,
On solving we get x = 9.5.
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