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In an examination, a student must secure 40% marks to pass. A student who gets 120 marks fails by 40 marks. What is the maximum marks for the examination?
400
500
300
600
400
Find the total passing marks by adding the score and failure gap (120 + 40 = 160). Since 160 represents 40%, simply calculate 100% by multiplying by 2.5 (or 160 / 0.4).
Student score = 120 marks, Failing margin = 40 marks, Passing percentage = 40%.
M=PS+FтАЛ├Ч100
Find the total passing marks by adding the score and failure gap (120 + 40 = 160). Since 160 represents 40%, simply calculate 100% by multiplying by 2.5 (or 160 / 0.4).
Many students subtract the failure gap (120 - 40) instead of adding it, as failing means they were short of the passing criteria.
Calculate total passing marks
Since the student scored 120 marks and failed by 40, the total marks required to pass is the sum of these values.
Passing┬аMarks=120+40=160
Set up the percentage equation
We know that 40% of the maximum marks (let it be M) equals the passing marks calculated above.
0.40├ЧM=160
Solve for Maximum Marks
Divide the passing marks by the passing percentage in decimal form to find M.
M=0.40160тАЛ=400
A is correct because the total marks required to pass is 160, which represents 40% of the maximum marks, leading to a total of 400.
This concept of 'Equating Values' is frequently used in Profit and Loss questions (e.g., selling price equals cost price plus profit percentage).
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