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Answer the questions given below based on the following data:A total of 250 students of a class play different games viz. Football, Hockey, Chess, Badminton, Table Tennis and Tennis. The ratio of girls to boys in the class of 250 is 13 : 12 respectively. 50% of the girls play Table Tennis and Badminton only. 20% of the boys play Football, Hockey and Tennis only. 15% of the boys play Tennis and Chess only. The ratio of number of girls to boys playing Tennis and Chess only is 2 : 3 respectively. 30% of the girls play Hockey and Chess only. 10% of the girls play Chess, Badminton and Table Tennis only. The remaining girls play only Football. Boys playing Table Tennis and Badminton only is 20% of the girls playing the same. 40% of the boys play only Football. The remaining boys play only Chess.What is the total number of students playing Football?
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By: anil on 05 May 2019 01.40 am
Total = 250 students Number of girls = $$frac{13}{13 + 12} imes 250 = 130$$ Number of boys = $$250 - 130 = 120$$ Girls playing only table tennis and badminton = $$frac{50}{100} imes 130 = 65$$ Girls playing hockey and chess only = $$frac{30}{100} imes 130 = 39$$ Girls playing chess, badminton and table tennis only = $$frac{10}{100} imes 130 = 13$$ Girls playing tennis and chess only = $$frac{18}{3} imes 2 = 12$$ Girls playing football only = $$130 - (65 + 39 + 13 + 12) = 1$$ Boys playing football, hockey and tennis only = $$frac{20}{100} imes 120 = 24$$ Boys playing tennis and chess only = $$frac{15}{100} imes 120 = 18$$ Boys playing table tennis and badminton = $$frac{20}{100} imes 65 = 13$$ Boys playing only football = $$frac{40}{100} imes 120 = 48$$ Boys playing only chess = $$120 - (24 + 18 + 13 + 48) = 17$$ $$ herefore$$ Total number of students playing football = 48 + 24 + 1 = 73
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