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Select the correct answerIn a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class ?Options302520Data inadequate

Question

Select the correct answerIn a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class ?Options302520Data inadequate

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Solution

The problem states that the number of boys and girls participating in the sports is in the ratio 3:2. It also states that the number of boys participating in the sports is 15.

Step 1: Determine the ratio value Since the ratio of boys to girls participating in sports is 3:2, and we know that 15 boys are participating, we can determine the value of the ratio. Each unit of the ratio represents 15/3 = 5 students.

Step 2: Determine the number of girls participating in sports Since each unit of the ratio represents 5 students, and the number of girls is represented by 2 units of the ratio, there are 2*5 = 10 girls participating in sports.

Step 3: Determine the number of boys not participating in sports The problem states that the number of girls not participating in the sports is 5 more than the number of boys not participating. Since we know that there are 60 students in total and 15 boys and 10 girls are participating in sports, we can determine the number of students not participating in sports. This is 60 - 15 - 10 = 35 students.

Step 4: Determine the number of boys and girls not participating in sports Let's denote the number of boys not participating in sports as x. According to the problem, the number of girls not participating in sports is x + 5. Since the total number of students not participating in sports is 35, we can write the equation x + (x + 5) = 35. Solving this equation gives x = 15. This means that there are 15 boys and 20 girls not participating in sports.

Step 5: Determine the total number of girls in the class The total number of girls in the class is the sum of the girls participating in sports and the girls not participating in sports. This is 10 + 20 = 30 girls.

So, the correct answer is 30.

This problem has been solved

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