Targeting an overall percentage: Three annual exams are each out of 500 marks. A student averaged 45% in the first and 55% in the second. To achieve an overall average of 60% across all three, how many marks are needed in the third exam?

Introduction / Context:
Weighted averages across equal-maximum exams reduce to totals. The overall target percentage dictates a target total; subtract known totals to find the remaining requirement.

Given Data / Assumptions:

• Three exams, each with 500 marks.
• Exam 1 average = 45% of 500.
• Exam 2 average = 55% of 500.
• Desired overall average = 60% across 1500 marks total.

Concept / Approach:
Total required = target percentage * grand total marks. Marks needed in exam 3 = required total minus (marks from exam 1 + exam 2).

Step-by-Step Solution:

Verification / Alternative check:
Totals become 225 + 275 + 400 = 900; 900/1500 = 0.60 = 60%.

Why Other Options Are Wrong:

• 450: Would give 950 total (63.33%).
• 350: Only 850 total (56.67%).
• 300: Just 800 total (53.33%).

Common Pitfalls:
Averaging the percentages directly without converting to totals can mislead when paper maxima differ; here they are equal but totals still keep logic clean.

Final Answer: