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In a community, 56% of the total families use mixers and 66% of the total use air conditioners.
What is the highest number of families not using either a mixer or an air conditioner?  
  • a)
    22%
  • b)
    24%
  • c)
    30%
  • d)
    34%
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In a community, 56% of the total families use mixers and 66% of the to...
Explanation:
Let's assume the total number of families in the community as 100.
Then, the number of families using mixers = 56% of 100 = 56
The number of families using air conditioners = 66% of 100 = 66

Families using both:
Now, we need to find the number of families using both mixers and air conditioners.
Let's assume the number of families using both as x.
Then, we have:
Number of families using mixers only = 56 - x
Number of families using air conditioners only = 66 - x

Total Families:
The total number of families using either mixers or air conditioners or both is given by the union of these sets: (mixers only) U (air conditioners only) U (both).
This can be written as:
Total number of families = (56 - x) + (66 - x) + x = 122 - x

Families not using either:
The number of families not using either mixers or air conditioners can be found as:
100 - (Total number of families using either mixers or air conditioners or both)
= 100 - (122 - x)
= x - 22

Highest number of families not using either:
To maximize the number of families not using either, we need to maximize x.
The maximum value of x can be obtained by assuming that all the families using mixers also use air conditioners.
That is, x = 56.
So, the highest number of families not using either mixers or air conditioners is:
x - 22 = 56 - 22 = 34
Therefore, the correct answer is option D, 34%.
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Community Answer
In a community, 56% of the total families use mixers and 66% of the to...
Highest number of families not using either a mixer or an air conditioner = 100 - 66 = 34%
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In a community, 56% of the total families use mixers and 66% of the total use air conditioners.What is the highest number of families not using either a mixer or an air conditioner?a)22%b)24%c)30%d)34%Correct answer is option 'D'. Can you explain this answer?
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