Question

In football championship, $153$ matches were played. Every team played one match with each other. The number of teams participating in the championship is-

• A. $17$
• B. $18$
• C. $9$
• D. None of these

Answer 1

Answer: (B)

$18$

Let the no$:$ of teams be $N$ namely $T_1,T_2,...T_N.$

Since each team played one game with the other game$,$ so $T_1$ played $(N-1)$games$,$ $T_2$ played $(N-2)$ games and so on$.$ Hence $,$ total no$:$ of games being played is given as $153$.

$⟹$ $153=\frac{N(N-1)}{2}$

$\therefore$ $N^2-N-306=0$

$\therefore$ $N=18$