A singles table tennis competition is played between class 10th and class 12th of a school. Every student had to play exactly one game with every other student. 45 games are played where both the players were of class 12th, and in 190 games both were from class 10. The number of games in which one player was a class 10 student and the other was a class 12 student is
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200 games in which one player was a class 10 student and the other was a class 12 student
Step-by-step explanation:
Let say There are n students in class
then 1st students will play against other n - 1 players
2nd students will play against other n - 2 players ( as his count with 1st player match has already been counted)
and so on
n- 1 , n-2 , n - 3 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 2 , 1 , 0
Total Games = n(n-1)/2
Class 12 Games = 45
=> n(n-1)/2 = 45
=> n(n-1) = 90
=> n = 10
Class 12 Students = 10
Class 10 Games = 190
=> n(n-1)/2 = 190
=> n(n-1) = 380
=> n = 20
Class 10 Students = 20
The number of games in which one player was a class 10 student and the other was a class 12 student
= 10 * 20
= 200
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