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%

.