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

A) 9.5

B) 10

C) 4.5

D) 6

Option (A)

As per CAT 2017 – Quantitative Aptitude – Arithmetic – Averages, we can see that

Score of girls = x

Score of boys = y

As per the question, x/30 = y/20 + 5

Average of class = (x + y)/ 50

New score of girls = xâ€™

New score of boys = yâ€™

x/30 â€“ 3 = xâ€™/30

(xâ€™ + yâ€™)/50 = (x + y)/50 + 2

xâ€™ = x â€“ 90

On solving we get, yâ€™ = y + 190

New average of boys = (y + 190)/20 = y/20 + 9.5

So, average of boys increases by 9.5

Option (A)

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