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Q.

In a chess tournament, all participants were to play one game with the other.  Two players fell ill after having played 3 games each.  If total number of games played in tournament is equal to 84.  Then total number of participants in the beginning was equal to 

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answer is 15.

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Detailed Solution

 n-2C2+6=84⇒n-2n-32=78⇒n2-5n+6-156=0 ⇒n2-5n-150=0 ⇒n-15n+10=0 ⇒n=15

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In a chess tournament, all participants were to play one game with the other.  Two players fell ill after having played 3 games each.  If total number of games played in tournament is equal to 84.  Then total number of participants in the beginning was equal to