In 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 ?
Question
In 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 ?
Solution
Step 1: We know that the number of boys participating in sports is 15.
Step 2: We also know that the ratio of boys to girls participating in sports is 3:2. So, we can set up the ratio as 15/x = 3/2.
Step 3: Solving for x (the number of girls participating in sports) gives us x = (15 * 2) / 3 = 10.
Step 4: We know that the number of girls not participating in sports is 5 more than the number of boys not participating. Since there are 15 boys participating, there are 60 - 15 = 45 boys not participating.
Step 5: Therefore, the number of girls not participating is 45 + 5 = 50.
Step 6: The total number of girls in the class is the number of girls participating in sports plus the number of girls not participating, which is 10 + 50 = 60.
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