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In a community, 56% of the total families use mixers and 66% of the total use air conditioners.
If the total number of families is 300, what is the number of families using air conditioners only?
- a)66
- b)132
- c)168
- d)188
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In a community, 56% of the total families use mixers and 66% of the to...
Understanding the Problem
In a community, we have the following information:
- Total families = 300
- Families using mixers = 56% of 300
- Families using air conditioners = 66% of 300
We need to find the number of families using air conditioners only.
Calculating Families Using Mixers and Air Conditioners
- Families using mixers:
56% of 300 = 0.56 * 300 = 168 families
- Families using air conditioners:
66% of 300 = 0.66 * 300 = 198 families
Using Venn Diagram Logic
Let's denote:
- A = Families using mixers
- B = Families using air conditioners
We know:
- |A| = 168 (using mixers)
- |B| = 198 (using air conditioners)
Let |A ∩ B| represent families using both appliances. Using the principle of inclusion-exclusion for the total families:
Calculating Total Families
- Total families = Families using mixers + Families using air conditioners - Families using both
300 = 168 + 198 - |A ∩ B|
Now, substituting the known values:
300 = 366 - |A ∩ B|
|A ∩ B| = 366 - 300 = 66 families (using both)
Finding Families Using Air Conditioners Only
Now, we can find families using air conditioners only:
- Families using air conditioners only = |B| - |A ∩ B|
= 198 - 66 = 132 families
Conclusion
Thus, the number of families using air conditioners only is 132, which corresponds to option 'B'.
In a community, we have the following information:
- Total families = 300
- Families using mixers = 56% of 300
- Families using air conditioners = 66% of 300
We need to find the number of families using air conditioners only.
Calculating Families Using Mixers and Air Conditioners
- Families using mixers:
56% of 300 = 0.56 * 300 = 168 families
- Families using air conditioners:
66% of 300 = 0.66 * 300 = 198 families
Using Venn Diagram Logic
Let's denote:
- A = Families using mixers
- B = Families using air conditioners
We know:
- |A| = 168 (using mixers)
- |B| = 198 (using air conditioners)
Let |A ∩ B| represent families using both appliances. Using the principle of inclusion-exclusion for the total families:
Calculating Total Families
- Total families = Families using mixers + Families using air conditioners - Families using both
300 = 168 + 198 - |A ∩ B|
Now, substituting the known values:
300 = 366 - |A ∩ B|
|A ∩ B| = 366 - 300 = 66 families (using both)
Finding Families Using Air Conditioners Only
Now, we can find families using air conditioners only:
- Families using air conditioners only = |B| - |A ∩ B|
= 198 - 66 = 132 families
Conclusion
Thus, the number of families using air conditioners only is 132, which corresponds to option 'B'.
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In a community, 56% of the total families use mixers and 66% of the total use air conditioners.If the total number of families is 300, what is the number of families using air conditioners only?a)66b)132c)168d)188Correct answer is option 'B'. Can you explain this answer?
Question Description
In a community, 56% of the total families use mixers and 66% of the total use air conditioners.If the total number of families is 300, what is the number of families using air conditioners only?a)66b)132c)168d)188Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a community, 56% of the total families use mixers and 66% of the total use air conditioners.If the total number of families is 300, what is the number of families using air conditioners only?a)66b)132c)168d)188Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a community, 56% of the total families use mixers and 66% of the total use air conditioners.If the total number of families is 300, what is the number of families using air conditioners only?a)66b)132c)168d)188Correct answer is option 'B'. Can you explain this answer?.
In a community, 56% of the total families use mixers and 66% of the total use air conditioners.If the total number of families is 300, what is the number of families using air conditioners only?a)66b)132c)168d)188Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a community, 56% of the total families use mixers and 66% of the total use air conditioners.If the total number of families is 300, what is the number of families using air conditioners only?a)66b)132c)168d)188Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a community, 56% of the total families use mixers and 66% of the total use air conditioners.If the total number of families is 300, what is the number of families using air conditioners only?a)66b)132c)168d)188Correct answer is option 'B'. Can you explain this answer?.
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