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In an exam, one candidate got 25% marks and failed by 40 marks while another candidate got 37% marks and got 20 marks more than the passing marks. What is the maximum marks of exam?
1. 500
2. 700
3. 400
4. 600

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Correct Answer - Option 1 : 500

Given:

One candidate got 25% marks and failed by 40 marks while another candidate got 37% marks and got 20 marks more than the passing marks.

Concept used:

% of pass candidate – % of fail candidate = Marks by which first candidate failed + marks by which another candidate passed

Calculation:

Let the maximum marks be x and the passing percentage be a.

Passing marks = a% of x = ax/100

First candidate obtained 25% of maximum marks and got 40 marks less than the passing marks.

⇒ (ax/100) – (25x/100) = 40

⇒ ax/100 = (25x/100) + 40      ----(i)

Another candidate obtained 37% of maximum marks and got 20 marks more than the passing marks.

⇒ (37x/100) = (ax/100) + 20

⇒ (ax/100) = (37x/100) – 20      ----(ii)

Solving equation (1) and (2)

⇒ (25x/100) + 40 = (37x/100) – 20

⇒ (37x/100) – (25x/100) = 40 + 20

⇒ 12x/100 = 60

⇒ x = (60 × 100)/12

⇒ x = 500 marks

∴ The maximum marks is 500

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