Correct Answer - Option 1 : 60%
Given:
First case: Sanny got marks = 45% of the total marks
But he failed by 75 marks
Second case: If he gets = 65% of the total marks
Then he will get 25 marks more than passing marks.
Concept used:
If a candidate got x marks and failed by y marks, then passing marks = x + y
If a candidate got x marks and got y marks more than passing marks, then passing marks = x - y
Passing percentage = (passing marks/total marks) × 100
Calculation:
Let the total marks be x.
Passing marks in the first case = [(45/100) × x] + 75
⇒ 0.45x + 75 ----(i)
And Passing marks in the second case = [(65/100) × x] - 25
⇒ 0.65x - 25 ----(ii)
From equation (i) and (ii), we get,
0.65x - 25 = 0.45x + 75
⇒ 0.65x - 0.45x = 75 + 25
⇒ 0.20x = 100
⇒ x = 100/0.20
⇒ x = 500 marks
Passing marks = 0.45x + 75
⇒ 0.45 × 500 + 75
⇒ 225 + 75
⇒ 300 marks
Passing percentage = (300/500) × 100
⇒ 300/5
⇒ 60%
∴ The passing percentage is 60%