Solution

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