Calculating Darshan's Combined Exam Percentage
This solution explains how to calculate the combined percentage of two exams based on the scores and maximum marks obtained.
Preliminary Exam Score Calculation
First, let's calculate the marks Darshan secured in the Preliminary exam.
- Percentage scored in Preliminary exam: 85%
- Maximum marks in Preliminary exam: 1200
- Marks obtained in Preliminary exam = $\frac{85}{100} \times 1200$
- Marks obtained in Preliminary exam = $85 \times 12 = 1020$ marks.
Main Exam Score Calculation
Next, we calculate the marks Darshan obtained in the Main exam.
- Percentage scored in Main exam: 70%
- Maximum marks in Main exam: 800
- Marks obtained in Main exam = $\frac{70}{100} \times 800$
- Marks obtained in Main exam = $70 \times 8 = 560$ marks.
Combined Percentage Calculation
To find the combined percentage, we need to sum the marks obtained in both exams and divide by the total maximum marks possible for both exams, then multiply by 100.
- Total marks obtained by Darshan = Marks in Preliminary + Marks in Main
- Total marks obtained = $1020 + 560 = 1580$ marks.
- Total maximum marks = Maximum marks in Preliminary + Maximum marks in Main
- Total maximum marks = $1200 + 800 = 2000$ marks.
- Combined Percentage = $\frac{\text{Total marks obtained}}{\text{Total maximum marks}} \times 100$
- Combined Percentage = $\frac{1580}{2000} \times 100$
- Combined Percentage = $\frac{158}{200} \times 100$
- Combined Percentage = $0.79 \times 100 = 79\%$.
Conclusion
Therefore, Darshan's combined percentage for both exams is 79%. This matches option 1.
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