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A candidate scores 25% and fails by 30 marks, while another candidate who scores 40% gets 15 marks more than the minimum passing marks. What is the maximum marks for the examination?
250
300
350
400
300
Equate the total difference in percentages (40% - 25% = 15%) to the total difference in marks (30 + 15 = 45 marks). Since 15% equals 45 marks, 1% equals 3 marks, and 100% equals 300 marks.
Candidate 1 scores 25% and fails by 30 marks. Candidate 2 scores 40% and exceeds passing marks by 15 marks.
Total┬аMarks=DifferenceinPercentageDifferenceinMarksтАЛ├Ч100
Equate the total difference in percentages (40% - 25% = 15%) to the total difference in marks (30 + 15 = 45 marks). Since 15% equals 45 marks, 1% equals 3 marks, and 100% equals 300 marks.
Students often subtract the marks instead of adding them, failing to account for the gap between a 'fail' zone (-30) and an 'exceed' zone (+15), which requires adding the magnitudes: 30 + 15 = 45.
Define the percentage and mark difference
Calculate the difference between the percentages and the total difference in marks required to cross the passing threshold.
40%тИТ25%=15%=30+15=45
Calculate the value of 1 percent
Divide the total mark gap by the percentage gap to find the value of 1 percent of the total.
1%=1545тАЛ=3
Find the maximum marks
Since 1 percent corresponds to 3 marks, the maximum marks (100 percent) is calculated by multiplying by 100.
100%=3├Ч100=300
B is correct because the difference of 15% in scores corresponds to a total of 45 marks, leading to a maximum of 300 marks.
This concept of 'difference of percentages equals difference of values' is frequently used in profit/loss and time-speed-distance problems where two scenarios are compared.