Comparing scored marks and given percentage: Aryan scored 350 marks. Vidya scored 76% in the same test and obtained 296 marks more than Aryan. What were the maximum marks of the test?

Introduction / Context:
Here we relate an absolute marks difference to a percentage score. Knowing one candidate’s raw score and the other candidate’s percentage plus the stated difference allows us to back out the maximum marks of the exam.

Given Data / Assumptions:

• Aryan’s marks = 350.
• Vidya’s marks = 76% of maximum = 0.76M.
• Vidya scored 296 more than Aryan ⇒ 0.76M = 350 + 296 = 646.

Concept / Approach:
Set up a single linear equation in the unknown maximum M using Vidya’s percentage relationship and the given difference with Aryan. Solve by dividing.

Step-by-Step Solution:

Verification / Alternative check:
Check Vidya’s marks: 76% of 850 = 0.76 * 850 = 646. Aryan’s marks = 350; difference = 646 − 350 = 296, matching the problem statement.

Why Other Options Are Wrong:

• 650, 900, 950: None of these yield Vidya’s marks as 646 at 76% or the stated difference of 296 when tested.

Common Pitfalls:
Adding 296 to 76% or mixing percent-of-maximum with a percent-of-Aryan’s marks. Keep the percentage tied to the maximum M, not to Aryan’s value.

Final Answer: