Average score of a class of 60 students in an examination is 43. If the…
2023
Average score of a class of 60 students in an examination is 43. If the average score of the students who have passed is 52 and that of those who have failed is 16, then what is the percentage of failed students?
Answer: A. 25% — CONCEPTFor two groups, each group total equals its average multiplied by its number of members. The combined total is the sum of the two group totals, and…
- A.
25%
- B.
28%
- C.
30%
- D.
20%
Show answer & explanation
Correct answer: A
CONCEPT
For two groups, each group total equals its average multiplied by its number of members.
The combined total is the sum of the two group totals, and combined average equals combined total divided by the total number of members.
APPLICATION
Let f be the number of failed students. Then the number of passed students is 60 − f.
The class total score is 60 × 43 = 2,580.
Using the two group averages, 52(60 − f) + 16f = 2,580.
Expanding gives 3,120 − 52f + 16f = 2,580, so 36f = 540 and f = 15.
Therefore, the failed-student percentage is (15 ÷ 60) × 100 = 25%.
CROSS-CHECK
With 45 passed and 15 failed students, the total is 45 × 52 + 15 × 16 = 2,580; dividing by 60 gives 43, the stated class average.