Multiple choice

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:

  1. 75.2

  2. 73.5

  3. 75.6

  4. 82.8
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C Correct answer
Explanation

With a 10:11 ratio of boys to girls among 42 students, there are 20 boys and 22 girls. Let the average score of the girls be g, making the boys' average score 1.2g. The total score of the class is 20 * 1.2g + 22 * g = 46g, which must equal 42 * 69 = 2,898, solving to g = 63. Thus, the average score of the boys is 1.2 * 63 = 75.6.

AI explanation

Using the given ratio of 10:11, there are 20 boys and 22 girls among the 42 students. Let the girls' average be x, making the boys' average 1.2x. The total score equation is 20(1.2x) + 22(x) = 42(69), which simplifies to 24x + 22x = 2898, so 46x = 2898. Solving for x gives the girls' average as 63, and 1.2 * 63 gives the boys' average of 75.6.

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