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A student scores 40% marks and fails by 20 marks. If he scores 50% marks, he gets 30 marks more than the passing marks. What is the maximum marks for the exam?
400
500
600
700
500
Simply divide the total mark gap (20 + 30 = 50) by the percentage gap (50% - 40% = 10%). Total marks = (50 / 10) * 100 = 500.
Student 1: 40% marks, fails by 20 marks. Student 2: 50% marks, exceeds passing by 30 marks.
Total┬аMarks=DifferenceinpercentageSumofmarksdifferenceтАЛ
Simply divide the total mark gap (20 + 30 = 50) by the percentage gap (50% - 40% = 10%). Total marks = (50 / 10) * 100 = 500.
Students often subtract the marks instead of adding them (20 - 30) or forget to convert the percentage difference into a decimal divisor.
Define variables
Let the maximum marks be M. Passing marks P can be expressed as P=0.4M+20 and also P=0.5MтИТ30.
0.4M+20=0.5MтИТ30
Equate and Solve
Rearrange the equation to solve for M by bringing the percentage terms on one side.
0.5MтИТ0.4M=20+30
Calculate Maximum Marks
Calculate the difference: 0.1M=50. Therefore, M=50/0.1.
M=500
B is correct because the difference of 10% marks corresponds to 50 marks, meaning 1% = 5 marks, so 100% = 500 marks.
This concept of 'Gap between two points' is frequently used in Time, Speed, and Distance problems where the time difference is given for different speeds.
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