A candidate scores 72% in one examination paper with a maximum of 900 marks and 80% in another paper with a maximum of 700 marks.\nIf the overall result is based on the combined percentage across both papers, what is the candidate combined percentage score?

Introduction / Context:
This question focuses on finding a combined percentage when a student appears in two different papers with different maximum marks. Rather than simply averaging the two percentage scores, we must use a weighted average based on the maximum marks in each paper. This situation is very common in school and competitive exams where subjects carry different weight, so understanding how to calculate the correct overall percentage is important for accurate result interpretation.

Given Data / Assumptions:

• First paper maximum marks = 900.
• Candidate scores 72% in the first paper.
• Second paper maximum marks = 700.
• Candidate scores 80% in the second paper.
• The final result is based on total marks obtained out of total maximum marks.
• We need the overall percentage scored across both papers combined.

Concept / Approach:
The key concept is weighted average. The candidate total marks are the sum of marks obtained in each paper. The total maximum marks are the sum of the two papers maximums. The combined percentage is then (total obtained marks / total maximum marks) * 100. We do not simply average 72% and 80%, because each percentage is calculated on a different base. Instead we convert each percentage to actual marks, add them, and divide by the combined maximum.

Step-by-Step Solution:
Step 1: Compute marks in the first paper: 72% of 900 = (72 / 100) * 900. Step 2: Calculate (72 / 100) * 900 = 0.72 * 900 = 648 marks. Step 3: Compute marks in the second paper: 80% of 700 = (80 / 100) * 700. Step 4: Calculate (80 / 100) * 700 = 0.80 * 700 = 560 marks. Step 5: Total marks obtained = 648 + 560 = 1208. Step 6: Total maximum marks = 900 + 700 = 1600. Step 7: Combined percentage = (total obtained / total maximum) * 100. Step 8: Combined percentage = (1208 / 1600) * 100. Step 9: Compute 1208 / 1600 = 0.755, so combined percentage = 75.5%.

Verification / Alternative check:
As a rough check, note that both percentages are above 70%, and the higher percentage (80%) is on the paper with fewer maximum marks. So the combined percentage should be between 72% and 80%, but closer to 72% because the 900 mark paper carries more weight. The result 75.5% lies between these values and is somewhat closer to 72% than to 80%, which makes intuitive sense. This confirms that the computed value is reasonable and consistent with the distribution of maximum marks.

Why Other Options Are Wrong:
A combined percentage of 76%, 76.5%, or 77% would correspond to higher total marks than 1208. Since the actual total is fixed once we calculate marks from each paper, these values cannot occur. For example a 76% combined score would require 0.76 * 1600 = 1216 marks, which is greater than 1208. Similarly 77% would require 1232 marks. Therefore only 75.5% exactly matches the candidate actual performance in both papers.

Common Pitfalls:
A frequent error is to average the two percentages directly, that is compute (72 + 80) / 2 = 76%. This ignores the different maximum marks and leads to an incorrect answer. Another mistake is to miscalculate one of the individual percentages in terms of marks. To avoid these problems, always convert each percentage to actual marks first, then sum them and compute one overall percentage from the totals.

Final Answer:
The candidate combined percentage score across both papers is 75.5%.