Discussion
Peter got 30% of the maximum marks in an examination and failed by 10 marks. However, Paul who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?
Answer: C
Let the maximum marks be M. Peter's 30% is 10 short of the pass mark, so pass marks = 0.3M + 10. Paul's 40% is 15 more than the pass mark, so \[0.4M=0.3M+10+15,\ \ 0.1M=25,\ \ M=250.\]
Pass marks = 0.3 x 250 + 10 = 85, option C. Check: 40% of 250 is 100, which is 15 above 85.
The pass mark is the same for both candidates, so the difference between 40% and 30%, which is 10% of M, equals the 25 marks that separate the two results.
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