CAT 2017 [slot 1] Question with solution 14

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