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Eduncle posted an MCQ
October 19, 2019 • 16:53 pm 0 points
  • CSIR NET
  • Life Sciences

In a group of students, 30% play only cricket, 20% play only football and 10% play only basketball. 20% of the students play both football and cricket,

In a group of students, 30% play only cricket, 20% play only football and 10% play only basketball. 20% of the students play both football and cricket, 15% play both basketball and cricket, 10% play both football and basketball. 15 students play no games, while 5% of the students play all three games. What is the total number of students ?

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    Eduncle Best Answer

    Let the total number of students = x
    Students playing only cricket = 30%
    Students playing only football = 20%
    Students playing only basketball = 10%
    So, students playing only one sport = 30 + 20 + 10 = 60% of x
    Students playing only cricket and football = 20% – 5%(who play all 3 sports) = 15%
    Students playing only football & basketball = 10% – 5% = 5%
    Students playing only basketball & cricket = 15% – 5% = 10%
    Students playing only 2 sports = 15% + 5% + 10% = 30%
    Students playing all 3 = 5%
    So students playing at least 1 sport = 60% + 30% + 5% = 95% of x
    Students playing no sport = 100 – 95 = 5% of x
    Given, 5% of x = 15
    So, x = 15 × 100/5 = 300 students

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