400 students took a mock test; 60% of the boys and 80% of the girls cleared…
2022
400 students took a mock test; 60% of the boys and 80% of the girls cleared the cut off in the test. If the total percentage of students clearing the cut off in the test is 65%, then how many girls appeared in the test?
Answer: A. 100 — CONCEPTWhen a total is divided into two groups, the overall percentage is the weighted average of the two group percentages. Equivalently, total successes…
- A.
100
- B.
120
- C.
150
- D.
300
Attempted by 5 students.
Show answer & explanation
Correct answer: A
CONCEPT
When a total is divided into two groups, the overall percentage is the weighted average of the two group percentages.
Equivalently, total successes equal the sum of the successes from the two groups.
APPLICATION
Let the number of girls be g. Then the number of boys is 400 − g.
Since 65% of 400 students cleared the cut-off, the total number who cleared it is 0.65 × 400 = 260.
The group totals give 0.80g + 0.60(400 − g) = 260.
Expanding and simplifying: 0.80g + 240 − 0.60g = 260, so 0.20g = 20 and g = 100.
CROSS-CHECK
If there are 100 girls, there are 300 boys.
The number clearing the cut-off is 80% of 100 plus 60% of 300 = 80 + 180 = 260, which is 65% of 400.
Therefore, 100 girls appeared in the test.