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 Badminton?
Total = 250 students
Number of girls = $$\frac{13}{13 + 12} \times 250 = 130$$
Number of boys = $$250 - 130 = 120$$
Girls playing only table tennis and badminton = $$\frac{50}{100} \times 130 = 65$$
Girls playing hockey and chess only = $$\frac{30}{100} \times 130 = 39$$
Girls playing chess, badminton and table tennis only = $$\frac{10}{100} \times 130 = 13$$
Girls playing tennis and chess only = $$\frac{18}{3} \times 2 = 12$$
Girls playing football only = $$130 - (65 + 39 + 13 + 12) = 1$$
Boys playing football, hockey and tennis only = $$\frac{20}{100} \times 120 = 24$$
Boys playing tennis and chess only = $$\frac{15}{100} \times 120 = 18$$
Boys playing table tennis and badminton = $$\frac{20}{100} \times 65 = 13$$
Boys playing only football = $$\frac{40}{100} \times 120 = 48$$
Boys playing only chess = $$120 - (24 + 18 + 13 + 48) = 17$$
$$\therefore$$ Number of students playing Badminton = 65 + 13 + 13
= 91
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