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In an examination a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?

Correct answer: D. 11

  • A. 8
  • B. 9
  • C. 10
  • D. 11

Explanation

The two corrections add 20 marks + 2 marks = 22 marks to the total. Since the average rises from 63 marks to 65 marks, the increase is 2 marks per paper, so the number of papers is 22 marks ÷ 2 marks per paper = 11 papers. The likely mistake is option c, which treats the 22 extra marks as if they were spread over 10 papers.

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An average represents the total of a set of values divided by the number of values, and a weighted average gives different importance to different groups. Problems involve missing values, combined averages, replacement of observations, and changes in the average, so the total and count must be tracked separately.

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