in a football championship 153 matches were played. every team played one match with each other. the number of team participating in the championship

Asked by Piyush Gupta | 9th Aug, 2010, 12:00: AM

Expert Answer:

Dear Student.
 
Let the number of teams be N namely T1, T2 , . . . TN.
Since, each team played one game with the other game, so T1 played (N-1) games, T2 played (N-2) games and so on.
 
Hence, total number of games being played is (N-1) + (N-2) + . . . + 1 + 0 = N(N-1)/2
 
The total number of games being played is given as 153.
 
=> 153 = N(N-1)/2
=> 306 = N2 - N
=> N2 - N - 306 = 0
 
Solving this quadratic equation, we get N = 18 or N = -17
But as number of teams can not be negative, therefore total number of teams in the tournament is 18.
 
 
Regards Topperlearning.

Answered by  | 30th Nov, 2017, 11:35: AM