In the Venn diagram above the very large circle represents all 290 club members. The circle containing regions A, D, F, G represents the tennis players. The circle containing regions B, E, F, G represents the chess players. The circle containing regions C, D, E, G represents the badminton players.
The regions are:
A Members who only play tennis
B Members who only play chess
C Members who only play badminton
D Members who play only tennis and badminton
E Members who play only chess and badminton
F Members who play only tennis and chess
G Members who play all three games
H Members who play none of the games
A+D+F+G=120
B+E+F+G=110
C+D+E+G=130
D+G=60, D=60-G
E+G=55, E=55-G
A+B+C+D+E+F+G+H=290.
A+F=120-(D+G)=60, B+F=110-(E+G)=55,
C+E=130-(D+G)=70, C+D=130-(E+G)=75,
C=70-E=70-(55-G)=15+G=75-D=75-(60-G),
The number playing tennis and chess is not given, that is, we don't know F+G. Let's represent this sum by n, F+G=n, F=n-G
So, since A+F=60, A=60-F=60-n+G, B+F=55, so B=55-F=55-n+G.
Now we have expressions for each region:
A=60-n+G, B=55-n+G, C=15+G, D=60-G, E=55-G, F=n-G, so n>G.
H=290-(A+B+C+D+E+F+G)=290-(A+(B+F)+(C+D)+(E+G))=290-(A+55+75+55)=105-A.
Also note that A+F=60, so F=60-A, which means that A<60. We can also see that G (the number playing all 3 games) must be less than 55.
There is insufficient information to find G.
For example, let A=35, then F=25, and let G=45, then B=55-70+45=30, C=60, D=15, E=10, H=70. This is only one solution of many because of the lack of information.