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In a club of 80 members, 10 members play none of the games Tennis, Badminton and Cricket. 30 members…

Out of 80 members, 10 play none of the games, so \( 80 - 10 = 70 \) play at least one game. Since 30 play exactly one game and 30 play exactly two games, the number playing…

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In a club of 80 members, 10 members play none of the games Tennis, Badminton and Cricket. 30 members play exactly one of these three games and 30 members play exactly two of these games. 45 members play at least one of the games among Tennis and Badminton, whereas 18 members play both Tennis and Badminton. The number of Cricket playing members is :

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Out of 80 members, 10 play none of the games, so 80−10=70 80 - 10 = 70 play at least one game. Since 30 play exactly one game and 30 play exactly two games, the number playing all three games is 70−30−30=10 70 - 30 - 30 = 10 . As shown in the figure, since 45 play Tennis or Badminton (or both), the number playing Cricket only is 70−45=25 70 - 45 = 25 ; those playing only Tennis and Badminton (without Cricket) are 18−10=8 18 - 10 = 8 , so those playing Cricket with exactly one other game are 30−8=22 30 - 8 = 22 . Therefore, the total number of Cricket-playing members is 25+22+10=57 25 + 22 + 10 = 57 .

Figure

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  • RPSC Rajasthan State and Subordinate Services (RAS/RTS)

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