In a chess competition involving some boys and girls of a school,every student had to play exactly one game wi

Question

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
(a) 200
(b) 216
(c) 235
(d) 256

Answer 1

The correct answer is a) 200

Explanation is very simple:
45 girls only games means there are 10 girls.
190 boys only games means there are 20 boys.

girl x boy games are 10x20 = 200.

I think this is more simple that jeorgans answer, so I deserve the 10 points :) Thanks

Answer 2

1

Answer 3

Let
g = number of girls
b = number of boys
gC2 = 45
g(g - 1)/2 = 45
g(g - 1) = 90
g² - g - 90 = 0
(g - 10)(g + 9) = 0
g = 10
Therefore there are 10 girls in the competition.

bC2 = 190
b(b - 1)/2 = 190
b(b - 1) = 380
b² - b - 380 = 0
(b - 20)(b + 19) = 0
b = 20
Therefore there are 20 boys in the competition.

There are 30 players in the competition, and there are a total of 30C2 games.
30C2 = 30(29)/2 = 15(29) = 435 games

Thus, there are 435 games all in all. Subtract the number of games in which there are both boys or both girls to get the number of games in which there are both a boy and a girl.
435 games - 45 games - 190 games = 200 games

.·. the answer is (a)200.

^_^

Answer 4

200 Games For Boys

Answer 5

a)

45 girls only games means there are 10 girls
(Sum for 1 to n of n-1)

190 boys only games means 20 boys.

10 *20 = 200


Checking:
30 participants means 435 games in total.

Substracting the pure gender games, we have 200 mixed gender games left.

Answer 6

the answer is A 200

Answer 7

option (c)=235

Answer 8

Wow, Thanks! I was asking myself the same thing today