In a chess competition involving some men and women, every player needs to play exactly one game with every other player. It was found that in 45 games, both the players were women and in 190 games, both players were men. What is the number of games in which one person was a man and other person was a woman? Select the correct option:
A) 40
B) 120
C) 180
D) 200
E) 220

Rationale: this is similar to handshake problem , if there are nn people , then number of handshakes = 1 + 2 + . . . n = n ∗ ( n − 1 ) / 2 no . of women be xx and given x ∗ ( x − 1 ) / 2 = 45 this gives x = 10 | | | y no . of men : solve y ∗ ( y − 1 ) / 2 = 190 . this gives y = 20 so total men vs . women = 10 * 20 = 200 . answer is d
Answer: D