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