UPSC Prelims 2011·CSAT·Quantitative Aptitude·Combinatorics and Probability

There are 100 students in a particular class. 60% students play cricket, 30% student play football and 10% student play both the games. What is the number of students who play neither cricket nor football?

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Last updated 23 May 2026, 3:31 pm IST
  1. A25
  2. B20Correct
  3. C18
  4. D15

Explanation

Here's a brief explanation: Total students = 100. Students playing Cricket = 60% of 100 = 60. Students playing Football = 30% of 100 = 30. Students playing Both games = 10% of 100 = 10. To find the number of students who play at least one game, we use the formula: Students (Cricket OR Football) = Students (Cricket) + Students (Football) - Students (Both) Students (Cricket OR Football) = 60 + 30 - 10 Students (Cricket OR Football) = 90 - 10 = 80. These 80 students play either cricket, or football, or both. The number of students who play neither game is: Total Students - Students (Cricket OR Football) 100 - 80 = 20. Therefore, 20 students play neither cricket nor football. Option A (25) is incorrect. Option B (20) is correct. Option C (18) is incorrect. Option D (15) is incorrect. The final answer is 20.
Quantitative Aptitude: There are 100 students in a particular class. 60% students play cricket, 30% student play football and 10% student play
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