In an examination, the average marks was found to be 40. For deducting marks…
2024
In an examination, the average marks was found to be 40. For deducting marks due to computational errors, the average marks of 100 candidates was changed from 80 to 40, hence the net average marks came down to 30. The total number of candidates, who appeared in the examination, was –
- A.
200
- B.
400
- C.
300
- D.
150
Show answer & explanation
Correct answer: B
Concept: When the marks of only a fixed subset of candidates are corrected, the overall average changes because the total marks change while the number of candidates stays the same. So (original total marks) minus (total marks removed by the correction) equals (new total marks), and dividing each side by the same candidate count links the old average and the new average.
Let the total number of candidates who appeared be m.
Since the original average was 40, the original total marks of all m candidates = 40m.
The average marks of the 100 candidates were corrected from 80 to 40, so their total marks fell from 100 × 80 = 8000 to 100 × 40 = 4000, a reduction of 8000 − 4000 = 4000.
The new total marks after the correction = 40m − 4000.
Since the net average became 30 for the same m candidates, the new total marks also equal 30m.
Equating the two expressions for the new total marks: 40m − 4000 = 30m, which gives m = 400.
Cross-check: With m = 400, the original total marks = 40 × 400 = 16000. Removing the 4000 marks corrected for the 100 candidates gives 16000 − 4000 = 12000, and 12000 / 400 = 30 — matching the given net average exactly.