Question
Find the total number of students who play Football.
Read the passage given below and answer the following questions. A school has a total of 990 students. Each student has to select at least 1 sport among Cricket, Football and Badminton. Students who play only Badminton are 50% of students who play only Football and ratio of students who play only Cricket to students who play only Badminton is 5:2. Students who play all 3 games together are 50% of students who play only Badminton. Students who play both Cricket and Badminton together are equal to students who play both Football and Badminton but not Cricket. Students who play both Cricket and Football but not Badminton are 50% more than students who play all 3 games together. Students who play both Cricket and Football but not Badminton are 50% of students who play both Football and Badminton together.Solution
Let students who play only Football be 20x. So, students who play only Badminton = 10x And, students who play only Cricket = 25x Now, students who play all 3 games together = 5x Now, students who play Cricket and Football but not Badminton = 7.5x And, students who play Football and Badminton together = 15x Now, students who play Football and Badminton but not Cricket = 10x Now, students who play both Cricket and Badminton together = 10x So, students who play Cricket and Badminton but not Football = 5x According to question, => 25x + 7.5x + 20x + 5x + 5x + 10x + 10x = 990 => x = 12 
Required number of students = 90 + 240 + 60 + 120 = 510
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