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In a town of 10000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families that buy none of these newspapers is
- a)4000
- b)4300
- c)4500
- d)5000
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
In a town of 10000 families, it was found that 40% families buy newsp...
To solve this problem, we can use the principle of inclusion-exclusion. Let's break down the given information step by step:
Step 1: Identify the given percentages:
- 40% families buy newspaper A.
- 20% families buy newspaper B.
- 10% families buy newspaper C.
- 5% families buy both A and B.
- 3% families buy both B and C.
- 4% families buy both A and C.
- 2% families buy all three newspapers.
Step 2: Calculate the number of families for each newspaper:
Let's assume there are 10,000 families in total.
- Number of families buying newspaper A = (40/100) * 10000 = 4000
- Number of families buying newspaper B = (20/100) * 10000 = 2000
- Number of families buying newspaper C = (10/100) * 10000 = 1000
Step 3: Calculate the number of families buying multiple newspapers:
Using the given percentages, we can calculate the number of families buying multiple newspapers.
- Number of families buying A and B = (5/100) * 10000 = 500
- Number of families buying B and C = (3/100) * 10000 = 300
- Number of families buying A and C = (4/100) * 10000 = 400
Step 4: Calculate the number of families buying none of the newspapers:
To find the number of families buying none of the newspapers, we need to subtract the total number of families buying any newspaper from the total number of families.
Total number of families buying any newspaper = Number of families buying A + Number of families buying B + Number of families buying C - Number of families buying A and B - Number of families buying B and C - Number of families buying A and C + Number of families buying all three newspapers.
Plugging in the values:
Total number of families buying any newspaper = 4000 + 2000 + 1000 - 500 - 300 - 400 + 200 = 6000
Number of families buying none of the newspapers = Total number of families - Total number of families buying any newspaper
Number of families buying none of the newspapers = 10000 - 6000 = 4000
Therefore, the correct answer is option A) 4000.
Step 1: Identify the given percentages:
- 40% families buy newspaper A.
- 20% families buy newspaper B.
- 10% families buy newspaper C.
- 5% families buy both A and B.
- 3% families buy both B and C.
- 4% families buy both A and C.
- 2% families buy all three newspapers.
Step 2: Calculate the number of families for each newspaper:
Let's assume there are 10,000 families in total.
- Number of families buying newspaper A = (40/100) * 10000 = 4000
- Number of families buying newspaper B = (20/100) * 10000 = 2000
- Number of families buying newspaper C = (10/100) * 10000 = 1000
Step 3: Calculate the number of families buying multiple newspapers:
Using the given percentages, we can calculate the number of families buying multiple newspapers.
- Number of families buying A and B = (5/100) * 10000 = 500
- Number of families buying B and C = (3/100) * 10000 = 300
- Number of families buying A and C = (4/100) * 10000 = 400
Step 4: Calculate the number of families buying none of the newspapers:
To find the number of families buying none of the newspapers, we need to subtract the total number of families buying any newspaper from the total number of families.
Total number of families buying any newspaper = Number of families buying A + Number of families buying B + Number of families buying C - Number of families buying A and B - Number of families buying B and C - Number of families buying A and C + Number of families buying all three newspapers.
Plugging in the values:
Total number of families buying any newspaper = 4000 + 2000 + 1000 - 500 - 300 - 400 + 200 = 6000
Number of families buying none of the newspapers = Total number of families - Total number of families buying any newspaper
Number of families buying none of the newspapers = 10000 - 6000 = 4000
Therefore, the correct answer is option A) 4000.
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Community Answer
In a town of 10000 families, it was found that 40% families buy newsp...
Number of families who buy none of A, B and C = N - n(A ∪ B ∪ C),
where N = Total number of families.
n(A): Number of Newspaper A readers.
n(B): Number of Newspaper B readers.
n(C): Number of Newspaper C readers.
Number of families who buy none of A, B and C = 10000 - {n(A) + n(B) + n(C) - n(A ⌒ B) - n(B ⌒ C) - n(A ⌒ C) + n(A ⌒ B ⌒ C)}
= 10000 - 4000 - 2000 - 1000 + 500 + 300 + 400 - 200
= 4000
Number of families who buy none of A, B and C = 4000
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In a town of 10000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families that buy none of these newspapers isa)4000b)4300c)4500d)5000Correct answer is option 'A'. Can you explain this answer?
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In a town of 10000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families that buy none of these newspapers isa)4000b)4300c)4500d)5000Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a town of 10000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families that buy none of these newspapers isa)4000b)4300c)4500d)5000Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a town of 10000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families that buy none of these newspapers isa)4000b)4300c)4500d)5000Correct answer is option 'A'. Can you explain this answer?.
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