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CAT 2017 Slot 1 — QA Question 14

AlligationEasy

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:

Answer & solution

  • 9.5

  • B

    10

  • C

    4.5

  • D

    6

Solution

Let the average score of the boys in the midsemester examination be b.
Average score of the girls = b + 5
Average of the class = 20b+30(b+5)50 = b + 3

New average of girls = (b + 5) - 3 = b + 2
Let new average of the boys = x

Average score of the entire class increased by 2 and is hence (b + 3) + 2 = b + 5

∴ 20x+30(b+2)50 = b + 5

⇒ 20x + 30b + 60 = 50b + 250
⇒ 20x = 20b + 190
⇒ x = b + 9.5

Increase in the average of boys is 9.5

Hence, option (a).

CAT 2017 Slot 1 QA Q14: A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was — Solution | TheCATExam