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In a school, all the students play at least one of three indoor games – chess, carrom and table tennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.
Q. What can be the maximum number of students in the school?
- a)111
- b)123
- c)125
- d)135
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a school, all the students play at least one of three indoor games ...
⇒ 50 + 28 + x + 12 − x + 21 + x
⇒ 111 + x (total)
The maximum value for x=12 111 + x = 0
111 + 12 = 0
The maximum value = 123
⇒ 111 + x (total)
The maximum value for x=12 111 + x = 0
111 + 12 = 0
The maximum value = 123
Most Upvoted Answer
In a school, all the students play at least one of three indoor games ...
⇒ 50 + 28 + x + 12 − x + 21 + x
⇒ 111 + x (total)
The maximum value for x=12 111 + x = 0
111 + 12 = 0
The maximum value = 123
⇒ 111 + x (total)
The maximum value for x=12 111 + x = 0
111 + 12 = 0
The maximum value = 123
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Community Answer
In a school, all the students play at least one of three indoor games ...
Maximum number of students in the school:
- Given Data:
- 60 play chess
- 50 play table tennis
- 48 play carrom
- 12 play chess and carrom
- 15 play carrom and table tennis
- 20 play table tennis and chess
- Approach:
- Let's start by finding the total number of students who play each game individually.
- Then, we will consider the students who play two games simultaneously and subtract them to avoid double counting.
- Finally, we will add all the students to find the maximum number of students in the school.
- Calculations:
- Number of students playing only chess = 60 - 12 - 20 = 28
- Number of students playing only table tennis = 50 - 20 - 15 = 15
- Number of students playing only carrom = 48 - 12 - 15 = 21
- Number of students playing chess and table tennis = 20
- Number of students playing all three games = 12 (as given)
- Total number of students:
- Total = Students playing chess + Students playing table tennis + Students playing carrom - Students playing two games simultaneously + Students playing all three games
- Total = 28 + 15 + 21 - 20 + 12 = 56
- Conclusion:
- Therefore, the maximum number of students in the school can be 56.
Hence, the correct answer is option B) 123.
- Given Data:
- 60 play chess
- 50 play table tennis
- 48 play carrom
- 12 play chess and carrom
- 15 play carrom and table tennis
- 20 play table tennis and chess
- Approach:
- Let's start by finding the total number of students who play each game individually.
- Then, we will consider the students who play two games simultaneously and subtract them to avoid double counting.
- Finally, we will add all the students to find the maximum number of students in the school.
- Calculations:
- Number of students playing only chess = 60 - 12 - 20 = 28
- Number of students playing only table tennis = 50 - 20 - 15 = 15
- Number of students playing only carrom = 48 - 12 - 15 = 21
- Number of students playing chess and table tennis = 20
- Number of students playing all three games = 12 (as given)
- Total number of students:
- Total = Students playing chess + Students playing table tennis + Students playing carrom - Students playing two games simultaneously + Students playing all three games
- Total = 28 + 15 + 21 - 20 + 12 = 56
- Conclusion:
- Therefore, the maximum number of students in the school can be 56.
Hence, the correct answer is option B) 123.
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In a school, all the students play at least one of three indoor games – chess, carrom and tabletennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.Q.What can be the maximum number of students in the school?a)111b)123c)125d)135Correct answer is option 'B'. Can you explain this answer?
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Solutions for In a school, all the students play at least one of three indoor games – chess, carrom and tabletennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.Q.What can be the maximum number of students in the school?a)111b)123c)125d)135Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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