The total papers = 15
Average marks of all 15 papers = 45
Average marks of first 8 papers (papers 1 to 8) = 48
Average marks of last 8 papers (papers 8 to 15) = 40
Total marks of all 15 papers:
Total=45×15
Total=675
Total marks of first 8 papers:
Total=48×8
Total=384
Total marks of last 8 papers:
Total=40×8
Total=320
The 8th paper appears in both the first 8 papers and the last 8 papers.
Adding the totals of first 8 and last 8 papers:
384+320=704
The difference between this sum and the actual total:
704−675=29
This difference represents the marks of the 8th paper, which was counted twice.
Therefore, the marks of the 8th paper = 29