In a school, half of students play badminton, one-fourth (1/4th) play volleyball, one-eighth (1/8th) play tennis, one-sixteenth (1/16th) play chess and remaining go for swimming. If the number of students playing volleyball is 160, how many students play chess ?

Question

Accepted Answer

To determine how many students play chess, we need to first understand the distribution of students across different sports based on the given information.

1. **Understanding the Distribution:**
   - Half of the students play badminton.
   - One-fourth (1/4th) of the students play volleyball.
   - One-eighth (1/8th) of the students play tennis.
   - One-sixteenth (1/16th) of the students play chess.
   - The remaining students go for swimming.

2. **Given Information:**
   - The number of students playing volleyball is 160.
   - Volleyball players represent one-fourth (1/4th) of the total students.

3. **Calculating Total Number of Students:**
   - Since 160 students represent one-fourth of the total, we can calculate the total number of students as follows:
     $$
     \text{Total students} = 160 \times 4 = 640
     $$

4. **Calculating Number of Students Playing Chess:**
   - Chess players represent one-sixteenth (1/16th) of the total students.
   - Therefore, the number of students playing chess is:
     $$
     \text{Chess players} = \frac{640}{16} = 40
     $$

5. **Explanation of Why Option 1 is Correct:**
   - Based on the calculation above, 40 students play chess, which matches Option 1.

6. **Explanation of Why Other Options are Incorrect:**
   - **Option 2 (120):** This would imply that one-sixteenth of the students is 120, which is incorrect because 120 is not one-sixteenth of 640.
   - **Option 3 (80):** This would imply that one-sixteenth of the students is 80, which is incorrect because 80 is not one-sixteenth of 640.
   - **Option 4 (20):** This would imply that one-sixteenth of the students is 20, which is incorrect because 20 is not one-sixteenth of 640.

In conclusion, the correct answer is Option 1, as the calculations show that 40 students play chess.