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In a class of 55 students, 34 like to play Cricket and 26 like to play Badminton. Also, each student likes to play at least one of the two games. How many students like to play both Cricket and Badminton?
- a)4
- b)5
- c)6
- d)3
- e)None of the above/More than one of the above
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In a class of 55 students, 34 like to play Cricket and 26 like to play...
Understanding the problem:
In a class of 55 students, 34 like to play Cricket and 26 like to play Badminton. Each student likes to play at least one of the two games. We need to find out how many students like to play both Cricket and Badminton.
Given data:
- Total number of students (n) = 55
- Number of students who like Cricket (C) = 34
- Number of students who like Badminton (B) = 26
Approach:
- We can use the formula: Total = Cricket + Badminton - Both + Neither
- Here, Total = 55 (Total number of students), Cricket = 34 (students who like Cricket), Badminton = 26 (students who like Badminton)
- Let x be the number of students who like both Cricket and Badminton.
- According to the formula: 55 = 34 + 26 - x + Neither
- Since each student likes at least one game, there are no students who like neither game. Therefore, we can simplify the equation to find x.
Solution:
- 55 = 34 + 26 - x
- 55 = 60 - x
- x = 60 - 55
- x = 5
Therefore, 5 students like to play both Cricket and Badminton. Hence, the correct answer is option B.
In a class of 55 students, 34 like to play Cricket and 26 like to play Badminton. Each student likes to play at least one of the two games. We need to find out how many students like to play both Cricket and Badminton.
Given data:
- Total number of students (n) = 55
- Number of students who like Cricket (C) = 34
- Number of students who like Badminton (B) = 26
Approach:
- We can use the formula: Total = Cricket + Badminton - Both + Neither
- Here, Total = 55 (Total number of students), Cricket = 34 (students who like Cricket), Badminton = 26 (students who like Badminton)
- Let x be the number of students who like both Cricket and Badminton.
- According to the formula: 55 = 34 + 26 - x + Neither
- Since each student likes at least one game, there are no students who like neither game. Therefore, we can simplify the equation to find x.
Solution:
- 55 = 34 + 26 - x
- 55 = 60 - x
- x = 60 - 55
- x = 5
Therefore, 5 students like to play both Cricket and Badminton. Hence, the correct answer is option B.
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Community Answer
In a class of 55 students, 34 like to play Cricket and 26 like to play...
The correct answer is option (2) i.e., 5 students.
Total students n(A U B) = 55
Students who like to play Cricket n(A) = 34
Students who like to play Badminton n(B) = 26
Formula used n(A U B) = n(A) + n(B) – n(A ∩ B)
students like to play both Cricket and Badminton n(A ∩ B) =
n(A) + n(B) - n(A U B) = 34 + 26 - 55 = 5
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In a class of 55 students, 34 like to play Cricket and 26 like to play Badminton. Also, each student likes to play at least one of the two games. How many students like to play both Cricket and Badminton?a)4b)5c)6d)3e)None of the above/More than one of the aboveCorrect answer is option 'B'. Can you explain this answer?
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