24 boys and a certain number of girls appeared for an exam. The average score of the boys was 42 and the average score of the girls was 34, while the combined average score was 38. How many girls appeared for the exam?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 24.
Boys = 24, average = 42 → total = 24 × 42 = 1008
Girls = x, average = 34 → total = 34 × x
Combined average = 38
Total students = 24 + x and Total marks = 1008 + 34x
Combined average = (Total marks) ÷ (Total students)
So:
38 = (1008 + 34x) ÷ (24 + x) ⇒ 38 × (24 + x) = 1008 + 34x ⇒ 912 + 38x = 1008 + 34x
⇒ 38x - 34x = 1008 - 912 ⇒ 4x = 96 ⇒ x = 24