There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84 , then the value of m is :

Step-by-step solution

Given, number of men is m and number of women is 2 . Since each participants competes two games with each other, Hence count of men Vs men total number of game plays = 2   m C 2 . count of men Vs women total number of game plays = 4 m . As per given condition in question, 2   m C 2 = 84 + 4   m ⇒ m 2 - 5   m - 84 = 0 ⇒ m 2 - 12   m + 7   m - 84 = 0 ⇒ m - 12 m + 7 = 0 . ⇒ m = 12 ,   - 7