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Question 17
A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is
Solution
Assume the number of members who can play exactly 1 game = I
The number of members who can play exactly 1 game = II
The number of members who can play exactly 1 game = III
I+2II+3III=144+123+132=399....(1)
I+II+III=256......(2)
=> II+2III=143.....(3)
Also, II+3III=58+25+63=146 ......(4)
=> III = 3 (From 3 and 4)
=> II =137
=> I = 116
The members who play only tennis = 123-58-25+3 = 43
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