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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

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Correct Answer - Option 1 : 9.5

Calculation:

⇒ Let be assume the score of the boy is x and the score of the girl is y.

⇒ According to question,

⇒ (y/30) - (x/20) = 5

⇒ Average of class = (x + y)/50

⇒ Let be assume new score of boys and girls is x' and y' respectively.

⇒ y/30 - y'/30 = 3

⇒ (x' + y')/50 - (x + y)/50 = 2

⇒ y' = y - 90

⇒ By solving we get x' = x + 190

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

⇒ The average increase by 9.5. 

∴ The required result will be 9.5.

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