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CAT 2017 [slot 1] Question with solution 14

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
Option: 1
Explanation:

Let the average score of girls in the mid semester exam be G.
Therefore the average score of boys in the mid semester exam is G-5.
Hence, the total marks scored by the class is 30×G+20×(G-5) = 50×G - 100

Therefore, the average of the entire class is (50G-100)/50 = G-2

Therefore, the average of girls in the final exam is G-3 and the average of the entire class in the final exam is G.
Hence, the total marks scored by the class is 50G, while the total marks scored by the girls is 30×(G-3)=30G-90

Therefore, the total marks scored by the boys is 50G-(30G-90) = 20G+90
Hence, the average of the boys in the final exam is (20G+90)/20 = G+4.5

Hence, the increase in the average marks of the boys is (G+4.5)-(G-5) = 9.5


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