Question

Question 20
All the students of a class participated in a tennis competition. Each student has to play with each of the other
student exactly once. In 300 of the games, both players were boys. In 120 of the games played, both players
were girls. Find the total number of matches played by the students of this class?
840
820
760
800​

Answer 1

option (b)

820 matches played by the students of this class.

Step-by-step explanation:

Number of games between two girls =   $\frac{x(x-1)}{2}$

Number of games between two boys =$\frac{y(y-1)}{2}$

given that: In 300 of the games, both players were boys. In 120 of the games played, both players  were girls.

$\frac{x(x-1)}{2} = 120\\ x(x-1) = 240\\x^2 -x=240\\x^2 - x - 240 = 0\\x^2 - 16x+15x-240 = 0\\x(x-16) +15(x-16) = 0\\(x-16) (x+15) = 0$

therefore , x= 16

$\frac{y(y-1)}{2} = 300\\ y(y-1) = 600\\y^2 -y=600\\y^2 - y - 600 = 0\\y^2 - 25y+24y-600 = 0\\y(y-25) +24(y-25) = 0\\(y-25) (y+24) = 0$

therefore y = 25

then, total number of games = $\frac{x+y (x+y-1)}{2}$

x+y = 25+16 = 41

= $\frac{41(40)}{2}$

= $\frac{1640}{2}$

=820

hence ,

option (b)

820 matches played by the students of this class.

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