All 120 students in a class play either cricket or football or both the games. Out of 120 students, 75 students play cricket only and 60 students play football only. How many students play both games ?

Question

All 120 students in a class play either cricket or football or both the games. Out of 120 students,  75 students play cricket only and 60 students play football only. How many students play both games ?

Accepted Answer

খ. 15

ব্যাখ্যা: **AI-লিখিত সর্বোত্তম অনুমানভিত্তিক ব্যাখ্যা — যাচাইকৃত মূল উত্তর নয়।**

মূল উৎসে 2 নম্বর বিকল্প চিহ্নিত আছে। নিশ্চিত বিকল্প নির্ণয় করা যায়নি; প্রকাশিত উত্তরসূচক অপরিবর্তিত রাখা হয়েছে।

স্পষ্ট অনুমান: Assuming 'only' is an error, n(C)=75, n(F)=60 gives n(C ∩ F) = 15

If 75 students play cricket ONLY and 60 play football ONLY, their sum is 75 + 60 = 135, which already exceeds the total number of students (120). Even if it meant 75 play cricket (total) and 60 play football (total), then n(C ∩ F) = 75 + 60 - 120 = 15. However, the problem explicitly states '75 students play cricket only and 60 students play football only', which is mathematically inconsistent (75 + 60 = 135 > 120). If the word 'only' was a typo in the original question, the answer would be 15 (Option 2).

উচ্চতর গণিত ১ম পত্র প্রশ্ন

সম্পর্কিত প্রশ্ন