JCECE Engineering JCECE Engineering Solved Paper-2014

  • question_answer
    There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 the number of games that the men played with the women. The number of participants is

    A)  6                                            

    B)  11

    C)  13                                         

    D)   None of these

    Correct Answer: C

    Solution :

    Let there be n men participants. Then, the number of games that the men play between themselves is \[2{{\cdot }^{n}}{{C}_{2}}\] and the number of games that the men played with the women is\[2\cdot (2n).\] \[\therefore \]  \[2{{\cdot }^{n}}{{C}_{2}}-2\cdot 2n=66\] \[\Rightarrow \]               \[n(n-1)-4n=66\] \[\Rightarrow \]               \[{{n}^{2}}-5n-66=0\] \[\Rightarrow \]               \[n=11\] \[\therefore \]Number of participants =11 men + 2 women =13


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