Q. In a chess tournament where the participants were to play one game with one another, two players fell ill having played 6 games each, without playing among themselves. If the total number of games is 117, then the number of participants at the beginning was
A) 15
B) 16
C) 17
D) 18
Explanation
(a)
Let the number of participants at the beginning was $n$
$\therefore\ \ \ \ \ \ \frac{n(n - 1)}{2} = 117 - 12$
$\Rightarrow \ \ \ n(n - 1) = 2 \times 105$
$\Rightarrow \ \ \ \ n^{2} - n - 210 = 0$
$\Rightarrow \ \ \ \ \ \ \ \ (n - 15)(n + 14) = 0$
$\Rightarrow \ \ \ \ \ n = 15\ \ \ \ \ \ \ \lbrack\because n \neq - 14\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.