Sets, Relations and FunctionsMCQPYQ Jun 23Question 1903 of 222
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A survey shows that $74\%\displaystyle of the Canadian like grapes, whereas $68\% like bananas. What percentage of the Canadians like both grapes and bananas, if everybody like either of two?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option d — $42\%$

All Options:

  • A$32\%$
  • B$26\%$
  • C6%\displaystyle 6\%
  • D$42\%$

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 ($100\%):<br><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>P</mi><mostretchy="false">(</mo><mi>G</mi><mo>∪</mo><mi>B</mi><mostretchy="false">)</mo><mo>=</mo><mn>100</mn><mimathvariant="normal">\displaystyle ):<br><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>G</mi><mo>∪</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mn>100</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">P(G \cup B) = 100\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">G</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">100%</span></span></span></span></span><br>We need to find the percentage of Canadians who like both grapes and bananas, which is the intersectionP(G \cap B)$.
Using the formula for the union of two sets:
P(G∪B)=P(G)+P(B)−P(G∩B)P(G \cup B) = P(G) + P(B) - P(G \cap B)100%=74%+68%−P(G∩B)100\% = 74\% + 68\% - P(G \cap B)100%=142%−P(G∩B)100\% = 142\% - P(G \cap B)P(G∩B)=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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