Study the given information and answer the questions that follow: A club has 63 members playing Cards, Chess and Carrom. 33 play Cards, 25 Chess and 26 Carrom. 10 play Cards and Chess, 9 play Carrom and Chess while 8 play both Cards and Carrom. Equal numbers play all three games as those who play none of the three. How many students played only one of the three games?Choices:- 34 39 35 37
Question
Study the given information and answer the questions that follow: A club has 63 members playing Cards, Chess and Carrom. 33 play Cards, 25 Chess and 26 Carrom. 10 play Cards and Chess, 9 play Carrom and Chess while 8 play both Cards and Carrom. Equal numbers play all three games as those who play none of the three. How many students played only one of the three games?Choices:- 34 39 35 37
Solution
To solve this problem, we can use the principle of inclusion and exclusion.
First, let's add up all the members who play each game: 33 (Cards) + 25 (Chess) + 26 (Carrom) = 84
Next, we subtract the number of members who play two games because we have counted them twice: 84 - 10 (Cards and Chess) - 9 (Carrom and Chess) - 8 (Cards and Carrom) = 57
However, we have subtracted the members who play all three games three times, so we need to add them back twice. We know that the number of members who play all three games is the same as the number of members who play none of the games. Let's denote this number as x.
So, the total number of members is: 57 + 2x = 63
Solving this equation for x gives us x = 3.
Therefore, the number of members who play only one game is: 33 (Cards) - 10 (Cards and Chess) - 8 (Cards and Carrom) + 25 (Chess) - 10 (Cards and Chess) - 9 (Carrom and Chess) + 26 (Carrom) - 8 (Cards and Carrom) - 9 (Carrom and Chess) - 3x = 34
So, the answer is 34.
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