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?
Aptitude
Average
Difficulty: Easy
Choose an option
Answer
Correct Answer: 400
Explanation
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:
Exam 1 = 0.45 * 500 = 225Exam 2 = 0.55 * 500 = 275Target total for 60% = 0.60 * 1500 = 900Needed in exam 3 = 900 - (225 + 275) = 900 - 500 = 400Verification / 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:
400