In a class the ratio of rural to urban students is 4 : 7. In an examination the average percentage marks of the rural and the urban
studentsare respectively 65 and 63. Whatis the overall average percentage marks of the class (correct to two decimal places)?
This questions was previously asked in
SSC CGL 17th August 2021 Shift-2
Explanation:
To find the overall average percentage marks of the class, follow these steps:
- Ratio Conversion: The ratio of rural to urban students is 4:7. Assume there are 4 rural students and 7 urban students, adding up to a total of 11 students.
- Calculate Contribution: Each rural student contributes 65% on average, and each urban student contributes 63% on average.
- Weighted Average Calculation:
\[
\text{Overall Average} = \left(\frac{4 \times 65 + 7 \times 63}{11}\right)
\]
- Calculating this gives:
- \( 4 \times 65 = 260 \)
- \( 7 \times 63 = 441 \)
- Total = \( 260 + 441 = 701 \)
- Divide by total students: \(\frac{701}{11} = 63.73\)
- Options Evaluation:
- Option 1: 63.73%
- Option 2: 65.87%
- Option 3: 64.37%
- Option 4: 73.63%
The correct answer is option 1. 63.73%
.
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By: santosh