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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 ?Options252030Data inadequate

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 ?Options252030Data inadequate

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Solution

Given:

  • Total number of students in the class = 60
  • Ratio of boys to girls participating in sports = 3:2
  • Number of boys participating in sports = 15
  • Number of girls not participating in sports is 5 more than the number of boys not participating in sports

Step-by-step solution:

  1. Let the number of boys participating in sports be 3x and the number of girls participating in sports be 2x.
  2. According to the problem, 3x = 15.
  3. Solving for x, we get x = 15 / 3 = 5.
  4. Therefore, the number of girls participating in sports = 2x = 2 * 5 = 10.
  5. Let the total number of boys in the class be B and the total number of girls be G.
  6. We know that B + G = 60.
  7. The number of boys not participating in sports = B - 15.
  8. The number of girls not participating in sports = G - 10.
  9. According to the problem, G - 10 = (B - 15) + 5.
  10. Simplifying, we get G - 10 = B - 10.
  11. Therefore, G = B.
  12. Since B + G = 60 and G = B, we have 2B = 60.
  13. Solving for B, we get B = 60 / 2 = 30.
  14. Therefore, G = 30.

So, the number of girls in the class is 30.

This problem has been solved

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