In class VI, 15\% of the 500 students participate in Dance and 8\% participate in Play. If 20\% of the students who participate in Dance also participate in Play, what is the ratio of students who participate only in Dance to those who participate only in Play?

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**Solution:**

1. Total students in class VI = 500

2. Students participating in Dance = 15\% of 500 = $ \frac{15}{100} \times 500 = 75 $

3. Students participating in Play = 8\% of 500 = $ \frac{8}{100} \times 500 = 40 $

4. Students who participate in both Dance and Play = 20\% of Dance participants = $ 20\% \times 75 = \frac{20}{100} \times 75 = 15 $

5. Students participating only in Dance = Total Dance participants - Both activities = $ 75 - 15 = 60 $

6. Students participating only in Play = Total Play participants - Both activities = $ 40 - 15 = 25 $

7. Required ratio = Only Dance : Only Play = $ 60 : 25 = 12 : 5 $

**Answer:** 12 : 5

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