Discussion

Explanation:

Let there be g girls and b boys.

Number of games between two girls = gC2​​​​​​​
∴ g(g – 1)/2 = 45 
⇒ g2 – g – 90 = 0
⇒ (g – 10)(g + 9) = 0
Since the number of girls cannot be negative, ∴ g = 10

Number of games between two boys = bC2
∴ b(b – 1)/2 = 190
⇒ b2 – b – 380 = 0
⇒ (b + 19)(b – 20) = 0
⇒ b = 20

∴ Number of games in which one player is a boy and the other is a girl = 10 × 20 = 200

Hence, option (a).

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