Multiple choice

In a competitive examination, the average marks obtained was 45. It was later discovered that there was some error in compurerisation and the marks of 90 candidates has to be changed from 80 to 50 and the average came down to 40 marks. The total number of candidates who appeared in examination is

  1. 520

  2. 550

  3. 540

  4. 560
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C Correct answer
Explanation

Changing each of 90 marks from 80 to 50 reduces the total by 90 × 30 = 2,700. The average falls by 5 marks, so the total number of candidates is 2,700/5 = 540.

AI explanation

The total reduction in marks is 90 candidates times 30 marks = 2700 marks. This reduction causes the overall average to drop by 5 marks, going from 45 to 40. The formula relating total change to average change is total change = total candidates times change in average. Setting up the equation gives 5 times N = 2700, so the total number of candidates is 2700 divided by 5, which equals 540.

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