Question

In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is

• A. \(215\)
• B. \(230\)
• C. \(200\)
• D. \(180\)
• E. \(250\)

Answer 1

The Correct Option is C

Concept: \[ \text{Number of games among } n \text{ players} = \binom{n}{2} \]
Step 1: Find number of girls.
\[ \binom{g}{2} = 45 \Rightarrow \frac{g(g-1)}{2} = 45 \Rightarrow g = 10 \]
Step 2: Find number of boys.
\[ \binom{b}{2} = 190 \Rightarrow \frac{b(b-1)}{2} = 190 \Rightarrow b = 20 \]
Step 3: Mixed games.
\[ g \times b = 10 \times 20 = 200 \]
Step 4: Option analysis.

• (A) Incorrect $\times$
• (B) Incorrect $\times$
• (C) Correct \checkmark
• (D) Incorrect $\times$
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (C).