The following table gives the marks (out of 100) of five students (i.e. A, B, C, D and E) over the years 2021 to 2025.STUDENTS NAME Year A B C D E 2021 75 82 75 84 74 2022 90 93 85 86 79 2023 96 76 65 85 85 2024 92 85 66 81 82 2025 86 82 73 80 83
Exam-Focused Solution: Marks Comparison Percentage Difference
Data Extraction and Summation
First, extract the marks for students A, B, C, and D from the table for the years 2021 to 2025.
| Student | 2021 | 2022 | 2023 | 2024 | 2025 | Total Marks |
|---|---|---|---|---|---|---|
| A | 75 | 90 | 96 | 92 | 86 | 439 |
| B | 82 | 93 | 76 | 85 | 82 | 418 |
| C | 75 | 85 | 65 | 66 | 73 | 364 |
| D | 84 | 86 | 85 | 81 | 80 | 416 |
Calculate the cumulative combined marks for each group:
- Students A and B: Total Marks = Total Marks of A + Total Marks of B = 439 + 418 = 857
- Students C and D: Total Marks = Total Marks of C + Total Marks of D = 364 + 416 = 780
Percentage Difference Calculation
Find the difference between the combined marks of (A+B) and (C+D):
Difference = Total (A+B) - Total (C+D) = 857 - 780 = 77
Calculate the percentage by which the marks of A and B are more than C and D:
Percentage = \(\frac{\text{Difference}}{\text{Total (C+D)}} \times 100\)
Percentage = \(\frac{77}{780} \times 100\)
Percentage \(\approx 0.0987 \times 100 \approx 9.87\%\)
Approximation and Final Answer
The question asks for the approximate percentage. Rounding 9.87% to the nearest whole number gives 10%.
Therefore, the marks scored by A and B together are more than those scored by C and D, by approximately 10%.
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