Question

In college B, each student participated in any one or both the sports, Hockey and Football. 36% of the students participated in both the sports. The number of students who participated in only Football is 120% more than those who participated in only Hockey. The total number of students who participated in only one of the sports is 960. What percentage of the students who participated in Hockey, participated in only Hockey?

• A. \(35\frac{5}{7}\)%
• B. 36%
• C. 35%
• D. 39%

Hint:

When a multi-part question is based on the same data set, keep your calculated values (like H, F, B, and Total students) handy as they will likely be needed for subsequent parts.

Answer 1

The Correct Option is A

Step 1: Utilize values from the prior calculation.
- Students in only Hockey (H) = 300.
- Students in only Football (F) = 660.
- Students in both (B) = 540.

Step 2: Determine the total Hockey participants.
Total Hockey = (Only Hockey) + (Both) = H + B = 300 + 540 = 840.

Step 3: Compute the required percentage.
Percentage = \( \left( \frac{\text{Only Hockey}}{\text{Total Hockey}} \right) \times 100 \).
Percentage = \( \left( \frac{300}{840} \right) \times 100 = \left( \frac{30}{84} \right) \times 100 = \left( \frac{5}{14} \right) \times 100 \).
Percentage = \( \frac{500}{14} = \frac{250}{7} = 35\frac{5}{7}% \).