Passing threshold and shortfall: To pass, 296 marks are required. A student secured 222 marks and is declared failed by 10% of the maximum marks. What are the maximum aggregate marks?

Introduction / Context:
This problem combines a fixed pass mark with a stated shortfall expressed as a percentage of the total maximum. The key is interpreting “failed by 10% marks” as being short by 10% of maximum marks, not 10% of the pass mark.

Given Data / Assumptions:

• Pass marks = 296.
• Obtained = 222.
• Shortfall = 296 − 222 = 74.
• Shortfall equals 10% of maximum M.

Concept / Approach:
Set 0.10M = 74 and solve for M. The pass threshold is provided only to determine the shortfall. Once M is found, no further adjustments are needed.

Step-by-Step Solution:

Verification / Alternative check:
10% of 740 = 74, which matches the stated shortfall; the student is indeed 74 below the required 296.

Why Other Options Are Wrong:

• 830, 810, 780: None make 10% equal to 74, so they cannot satisfy the “failed by 10%” condition.

Common Pitfalls:
Interpreting “failed by 10%” as 10% of the pass mark (296), which would give 29.6—incorrect by the problem’s phrasing that references maximum marks.

Final Answer: