Explanation:

- The total number of students is 42.

- Their average score is 69.

- The ratio of boys to girls is 10:11.

- Let the number of boys be \(10x\) and girls be \(11x\).

- Solving \(10x + 11x = 42\), we find \(x = 2\).

- Number of boys = 20, and number of girls = 22.

- Overall total score = 42 * 69 = 2898.

- Let the average score of girls be \(g\).

- The boys' average is 20% more, so \(1.2g\).

- Total boys' score \(= 20 \times 1.2g = 24g\).

- Total girls' score \(= 22 \times g = 22g\).

- Total score equation: \(24g + 22g = 2898\).

- Solving, \(46g = 2898\), so \(g = 63\).

- Average score of boys \(= 1.2 \times 63 = 75.6\).

- Option 3: 75.6 is the correct average score of the boys. .