P&C-8 (CAT-2005)

In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is:

(1)200   (2) 216   (3) 235   (4) 256

Solution follows here:

Solution:

Let the number of boys be ‘b’ and the number of girls be ‘g’.

Number of matches in which both are girls = gC2 = 45

g(g-1)/2 = 45 = g(g-1) = 90 = 10*9 => g = 10

Number of matches in which both are boys = bC2 = 190

b(b-1)/2 = 190 = b(b-1) = 380 = 20*19 => b = 20

The number of games in which one player was a boy and the other was a girl

= bC1 * gC1 = 20C1 * 10C1 = 20*10 = 200

Answer (1)