Sets, Relations and FunctionsMCQPYQ Jun 23Question 1903 of 217
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A survey shows that 74%\displaystyle 74\% of the Canadian like grapes, whereas 68%\displaystyle 68\% like bananas. What percentage of the Canadians like both grapes and bananas, if everybody like either of two?

Options

A32%\displaystyle 32\%
B26%\displaystyle 26\%
C6%\displaystyle 6\%
D42%\displaystyle 42\%
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Correct Answer

Option d42%\displaystyle 42\%

All Options:

  • A32%\displaystyle 32\%
  • B26%\displaystyle 26\%
  • C6%\displaystyle 6\%
  • D42%\displaystyle 42\%

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Detailed Solution & Explanation

Let G\displaystyle G represent the set of Canadians who like grapes, and B\displaystyle B represent the set of Canadians who like bananas.
We are given the following percentages:
P(G)=74%P(G) = 74\%
P(B)=68%P(B) = 68\%
The statement "everybody likes either of the two" implies that the union of these two groups accounts for the entire population (100%\displaystyle 100\%):
P(GB)=100%P(G \cup B) = 100\%
We need to find the percentage of Canadians who like both grapes and bananas, which is the intersection P(GB)\displaystyle P(G \cap B).
Using the formula for the union of two sets:
P(GB)=P(G)+P(B)P(GB)P(G \cup B) = P(G) + P(B) - P(G \cap B)100%=74%+68%P(GB)100\% = 74\% + 68\% - P(G \cap B)100%=142%P(GB)100\% = 142\% - P(G \cap B)P(GB)=142%100%=42%P(G \cap B) = 142\% - 100\% = 42\%
Hence, **Option D** 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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