The average score obtained by 64 boys and a certain number of girls in a test is 59.15, while the average score obtained by the boys is 55.25. If the average score of the girls is 68.75, then how many girls appeared for the test?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 26.
Let the number of girls be x
Total score of 64 boys = 64 × 55.25 = 3,536
Total score of x girls = x × 68.75
Total score of all students = 59.15 × (64 + x)
According to the question,
3,536 + 68.75x = 59.15(64 + x)
⇒ 3,536 + 68.75x = 3,785.6 + 59.15x
⇒ 68.75x − 59.15x = 3,785.6 − 3,536
⇒ 9.6x = 249.6
⇒ x = 249.6 ÷ 9.6
⇒ x = 26 girls