What is the ratio of number of girls playing Hockey to the number of boys playing Hockey respectively?

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 = $$120 - (24 + 18 + 13 + 48) = 17$$

=> Number of girls playing hockey = 39

Number of boys playing hockey = 24

$$\therefore$$ Required ratio = 39 : 24

= 13 : 8