CAT 2017Slot 1QAQuestion & Solution
Question
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
Options
9.5
10
4.5
6
Solution
Let, the average score of boys in the mid semester exam is A.
Therefore, the average score of girls in the mid semester exam be A+5.
Hence, the total marks scored by the class is $20\times (A) + 30\times (A+5) = 50\times A + 150$
The average score of the entire class is $\dfrac{(50\times A + 150)}{50} = A + 3$
wkt, class average increased by 2, class average in final term $= (A+3) + 2 = A + 5$
Given, that score of girls dropped by 3, i.e $(A+5)-3 = A+2$
Total score of girls in final term $= 30\times(A+2) = 30A + 60$
Total class score in final term $= (A + 5)\times50 = 50A + 250$
the total marks scored by the boys is $(50A + 250) - (30A - 60) = 20A + 190$
Hence, the average of the boys in the final exam is $\dfrac{(20G + 190)}{20} = A + 9.5$
Hence, the increase in the average marks of the boys is $(A+9.5) - A = 9.5$