Among a group of n persons, number of matches played
=n(n−1)/2 Among the Junior participants, let the number of girls be
n.
The number of matches played among girls
=n(n−1)/2=153 ⇒n(n−1)=306=18×17⇒n=18
Number of boys
=43−18=25 The number of matches played between a boy and a girl
=25×18=450 Among the Senior level participants, let the number of boys be
n.
The number of matches played between two boys
=n(n−1)/2=276 ⇒n(n−1)=552=24×23⇒n=24
The number of girls
=51−24=27 The number of matches played between a boy and a girl
=27×24=648 Required answer
=450+648=1098