Determine the ratio of the number of students who play Football to the number of students who play Basketball in a survey of 120…

Question

Determine the ratio of the number of students who play Football to the number of students who play Basketball in a survey of 120 students from the following table:

1. A. 6 : 7
2. B. 7 : 5
3. C. 7 : 6 (Correct answer)
4. D. 5 : 7

Correct Answer

Option C — 7 : 6

Detailed Solution & Explanation

The correct answer is 7 : 6.

Key Points

• Read the categories carefully — "plays Football" includes everyone who plays it, whether or not they also play Basketball:
  • Football total = plays both (25) + Football only (45) = 70
  • Basketball total = plays both (25) + Basketball only (35) = 60
• The ratio is 70 : 60 = 7 : 6.

Additional Information

• Check the table totals: 25 + 45 + 35 + 15 = 120, matching the surveyed number, which confirms the categories are exhaustive and non-overlapping.
• In set notation, n(F ∪ B) = n(F) + n(B) − n(F ∩ B) = 70 + 60 − 25 = 105, and the remaining 15 play neither.
• The intended error is to use only the "but not" rows, giving 45 : 35 = 9 : 7. The overlap category belongs to both totals, and that is precisely what the question is testing.

प्रश्न (हिन्दी में)

120 छात्रों के सर्वेक्षण से, निम्नलिखित तालिका के आधार पर फुटबॉल खेलने वाले छात्रों की संख्या और बास्केटबॉल खेलने वाले छात्रों की संख्या का अनुपात ज्ञात कीजिए:

1. A. 6 : 7
2. B. 7 : 5
3. C. 7 : 6
4. D. 5 : 7