NIMCET 2019 Question Paper with solutions

Question : 23 of 120

Marks: +1, -0

In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every of her player. Also, the total number of gam es played by the men among themselves exceeded by 66 the number of gam es that the men played against the women. Then the total number of players in the tournament is

Validate

Solution:

We have, n men and 2 women
Total number of games played by men among themselves

2⋅^nC_2={2(n)(n-1)}/2

=n^2-n

Total number of games played by men against women

=2(2n)=4n

∴\;n^2-n=4n+66

⇒n^2-5n-66=0

(n-11)(n+6)=0

n=11

n≠-6

∴ Total number of players

=11+2=13

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