In a carom tournament in school all the kids played against each other exactly once. The number of games involving a girl and a boy is 150 and the number of games involving two girls is 60 less than the number of games involving two boys, find the total strength of the school?

Let the number of boys in the class= B

number of girls in the class = G.

"The number of games involving a girl and a boy is 150" ==> Bc1*Gc1 = 150 ==> B*G = 150 --- (1)

"the number of games involving two girls is 60 less than the number of games involving two boys" ==> Gc2 +60 =Bc2 ==> G(G-1) + 120 = B(B-1) --- (2)

By solving equations (1), (2) we can deduce the values of B, G.

B=15, G=10.

So the total strength of the class = 10+15 = 25.