Sets, Relations and FunctionsMCQMTP June 24 Series IIQuestion 1939 of 217
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In a town of 20,000 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 newspaper, then the number of families which buy A only is

Options

A6600
B6300
C6000
D5600
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Correct Answer

Option a6600

All Options:

  • A6600
  • B6300
  • C6000
  • D5600

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Detailed Solution & Explanation

Let N=20,000\displaystyle N = 20,000 be the total number of families.
Let A\displaystyle A, B\displaystyle B, and C\displaystyle C represent the sets of families buying newspapers A, B, and C respectively.
We are given the percentages of families buying the newspapers:
- P(A)=40%\displaystyle P(A) = 40\%
- P(B)=20%\displaystyle P(B) = 20\%
- P(C)=10%\displaystyle P(C) = 10\%
- P(AB)=5%\displaystyle P(A \cap B) = 5\%
- P(BC)=3%\displaystyle P(B \cap C) = 3\%
- P(AC)=4%\displaystyle P(A \cap C) = 4\%
- P(ABC)=2%\displaystyle P(A \cap B \cap C) = 2\%
We want to find the number of families that buy newspaper A only. The percentage of families buying A only is:
P(A only)=P(A)P(AB)P(AC)+P(ABC)P(\text{A only}) = P(A) - P(A \cap B) - P(A \cap C) + P(A \cap B \cap C)
Substituting the values:
P(A only)=40%5%4%+2%=33%P(\text{A only}) = 40\% - 5\% - 4\% + 2\% = 33\%
The number of families is:
Number of families=33% of 20,000\text{Number of families} = 33\% \text{ of } 20,000
Number of families=0.33×20,000=6,600\text{Number of families} = 0.33 \times 20,000 = 6,600
Hence, **Option A** is the correct answer.

About This Chapter: Sets, Relations and Functions

Paper

Paper 3: Quantitative Aptitude

Weightage

3-5 Marks

Key Topics

Sets, Relations, Functions

This chapter covers Sets, Relations, Functions and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 3-5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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