JEE Main 2020MathematicsSets and RelationsEasyMCQ

JEE Main 2020 — Sets and Relations Question with Solution

JEE Main 2020 (05 Sep Shift 1)

Question

A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be:

Choose an option

Show full solutionCorrect option: B
Correct answer
B36

Step-by-step explanation

nC=73, nT=65, nC∩T=x, 

Considering that value of nC∪T cannot exceed 100 in terms of percentage, we get

nC∪T≤100

⇒  nC+nT-nC∩T≤100

⇒  x≥38

Therefore, x≠36.

nC∩T≤minnC,nT ⇒ x≤65

⇒ 38≤x≤65

Hence x may assume values 63,54,38.

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About this question

This is a previous-year question from JEE Main 2020, covering the Sets and Relations chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.