John got 20% marks in an examination and failed by 10 marks. In the same examination, Jack got 35% marks which were 20 more than the minimum passing marks, Find the percentage of minimum marks required to pass.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 25.
Let T be the total marks of the examination.
Let P be the minimum passing mark.
John got 20% of the total marks and failed by 10 marks:
John’s marks = 0.20T
0.20T + 10 =P
Jack got 35% of the total marks and his marks were 20 more than the minimum passing marks:
Jack’s marks=0.35T
0.35T = P + 20
We have two equations:
- 0.20T + 10 = P
- 0.35T = P + 20
Substitute P from the first equation into the second equation:
0.35T = (0.20T + 10) + 20
0.35T = 0.20T + 30
Subtract 0.20T from both sides:
0.15T = 30
T = 30/0.15
T = 200
Put the value of T = 200 into the first equation:
P = 0.20 × 200 + 10
P = 50
Percentage of passing marks = P/T × 100
Percentage of passing marks = 50/200 × 100
Percentage of passing marks = 25%