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 In a school, 40 % of the students play football and 50 % play cricket. If 18 % of the students play neither football nor cricket, the percentage of students playing both is
  • a)
    40 %
  • b)
    32 %
  • c)
    22 %
  • d)
    8 %
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In a school, 40 % of the students play football and 50 % play cricket....
Let A = set of students who play football and 
B = set of students play cricket. 
Then n(A) = 40, n (B) = 50 and 
n(A U B) = (100 - 18) = 82 
n(A U B) = n(A) + n(B) “ n(A ∩ B) 
n(A∩B) = n(A) + n(B) “ n(AUB) = (40 + 50 -82) = 8 
Percentage of the students who play both = 8%
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Most Upvoted Answer
In a school, 40 % of the students play football and 50 % play cricket....
Let A = set of students who play football and 
B = set of students play cricket. 
Then n(A) = 40, n (B) = 50 and 
n(A U B) = (100 - 18) = 82 
n(A U B) = n(A) + n(B) “ n(A ∩ B) 
n(A∩B) = n(A) + n(B) “ n(AUB) = (40 + 50 -82) = 8 
Percentage of the students who play both = 8%
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Community Answer
In a school, 40 % of the students play football and 50 % play cricket....

Explanation:

Given Data:
- Percentage of students playing football = 40%
- Percentage of students playing cricket = 50%
- Percentage of students playing neither football nor cricket = 18%

Calculation:
Let's assume:
- Number of students playing football = F
- Number of students playing cricket = C

From the given data:
- Number of students playing both football and cricket = x

The total percentage of students playing football or cricket can be calculated as:
Total = Football + Cricket - Both + Neither

Substitute the given values:
100 = 40 + 50 - x + 18
100 = 90 - x + 18
x = 8

Therefore, the percentage of students playing both football and cricket is 8%.

So, the correct answer is option D) 8%.
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