The average score of 42 students in a test is 69. The ratio of the number of boys to that of girls is 10 : 11. The average score of the boys is 20% more than that of the girls. The average score of the boys is:

75.6

Lets assume average score of girls be 5x

Average score of boys = 1.20 x avg. score of girls

                                 = 5x x \(\frac{120}{100}\) = 5x x \(\frac{6}{5}\) = 6x

Number of boys = 42 x \(\frac{10}{21}\) = 20

Number of girls = 42 x \(\frac{11}{21}\) = 22

According to question,

6x x 20 + 5x × 22 = 69 x 42

60x + 55x = 69 x 21

115x = 1449

x = 12.6

Average score of boys = 6 x 12.6 = 75.6