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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 ?Options252030Data inadequate

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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 ?Options252030Data inadequate

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Solution 1

The problem states that the ratio of boys to girls participating in sports is 3:2. We know that the number of boys participating in sports is 15.

Step 1: Determine the number of girls participating in sports. Since the ratio of boys to girls is 3:2, and we know there are 15 boys, we can set up the following equation: 15/3 = x/2. Solving for x gives us 10. So, there are 10 girls participating in sports.

Step 2: Determine the number of students not participating in sports. The total number of students in the class is 60. We know that 15 boys and 10 girls are participating in sports, so the number of students not participating in sports is 60 - 15 - 10 = 35.

Step 3: Determine the number of boys and girls not participating in sports. The problem states that the number of girls not participating in sports is 5 more than the number of boys not participating. Let's denote the number of boys not participating as y. Then the number of girls not participating is y + 5. Since the total number of students not participating is 35, we can set up the following equation: y + (y + 5) = 35. Solving for y gives us 15. So, there are 15 boys and 20 girls not participating in sports.

Step 4: Determine the total number of girls in the class. The total number of girls in the class is the number of girls participating in sports plus the number of girls not participating in sports. So, the total number of girls is 10 + 20 = 30.

So, the correct answer is 30.

This problem has been solved

Solution 2

The number of boys participating in the sports is given as 15. Since the ratio of boys to girls participating in the sports is 3:2, this means that the number of girls participating in the sports is (2/3) * 15 = 10.

The problem also states that the number of girls not participating in the sports is 5 more than the number of boys not participating. Since there are 15 boys participating, this means there are 60 - 15 = 45 boys not participating. Therefore, there are 45 + 5 = 50 girls not participating.

So, the total number of girls in the class is the number of girls participating in the sports plus the number of girls not participating, which is 10 + 50 = 60.

Therefore, the correct answer is "Data inadequate".

This problem has been solved

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