To solve this problem, let's assume the maximum marks as 'x'.
According to the given information:
- The first candidate gets 20% marks and fails by 10 marks. This means that the first candidate scored 20% of x, which is (20/100) * x = 0.2x. Since the first candidate fails by 10 marks, we can write the equation as:
0.2x - 10 = 0
- The second candidate gets 42% marks, which is (42/100) * x = 0.42x. The second candidate gets 12% more than the passing marks, so we can write the equation as:
0.42x - passing marks = 1.12 * passing marks
Simplifying it, we get:
0.42x - passing marks = 1.12 * passing marks
0.42x = 2.12 * passing marks
passing marks = (0.42x) / 2.12
Since the first candidate fails, the passing marks should be equal to or less than the marks obtained by the first candidate.
Now, substituting the value of passing marks in the equation, we get:
(0.42x) / 2.12 <= 0.2x
Simplifying it further:
0.42x <= 0.2x * 2.12
0.42x <= 0.424x
0.004x <= 0
Since x cannot be negative, we can conclude that x = 0.
But the maximum marks cannot be 0, so this is not a valid solution.
Therefore, the only possible answer is that there is no maximum marks value that satisfies all the given conditions.
Hence, the correct answer would be None of the above.