In an examination, a candidate secured 504 marks out of a maximum mark M. If the maximum mark M is scaled so that it becomes 800, the candidate would have secured 384 marks. What is the value of M?

Introduction / Context:
This question examines proportional reasoning and scaling of marks. A candidate's performance is expressed as a fraction of the maximum marks. When the maximum possible marks change due to scaling, the candidate's marks change in the same proportion. By equating the performance fractions before and after scaling, we can solve for the original maximum mark M. The twist is that the correct numerical value does not appear directly among the numeric options, so careful interpretation of the option “None of the above” is required.

Given Data / Assumptions:

• Original score of the candidate = 504 marks.
• Original maximum marks = M.
• After scaling, maximum marks become 800.
• Scaled score of the candidate would then be 384 marks.
• The candidate's performance fraction remains the same under scaling.

Concept / Approach:
The fraction of marks obtained is score divided by maximum marks. Initially, this fraction is 504 / M. After scaling, the fraction is 384 / 800. Since both fractions represent the same performance, we set them equal and solve for M. Once the value of M is found, we compare it with the listed numeric options. If it does not match, then the correct choice is “None of the above”.

Step-by-Step Solution:
Performance before scaling: 504 / M. Performance after scaling: 384 / 800. Equate the fractions: 504 / M = 384 / 800. Cross multiply: 504 * 800 = 384 * M. Compute left side: 504 * 800 = 403200. So 403200 = 384 * M. Therefore M = 403200 / 384. Simplify the division to obtain M = 1050.

Verification / Alternative check:
Check the fractions with M = 1050. The original performance is 504 / 1050, which simplifies to 0.48. The scaled performance is 384 / 800, which also equals 0.48. Since these are equal, M = 1050 is consistent. Now, comparing with the numeric options 910, 1000 and 970, none of them equals 1050, so the correct option is that none of the listed numeric values matches the true maximum mark.

Why Other Options Are Wrong:
Choosing 910, 1000 or 970 would produce a performance fraction different from 384 / 800. If M were 1000, for example, 504 / 1000 would be 0.504, which is not equal to 0.48. Similar discrepancies appear for 910 and 970. Only M = 1050 yields the correct equality between the two performance fractions.

Common Pitfalls:
A typical mistake is to assume M is 800 or to misinterpret scaling as simple addition instead of proportional change. Another error is to stop after computing M and pick the closest numeric option instead of recognizing that the correct value is absent and that the “None of the above” choice must be used. Always verify proportional relationships carefully when options include such a choice.

Final Answer:
The original maximum mark M is 1050, so the correct choice is None of the above.