JEE Mains · Maths · STD 11 - 1. set theory
In a certain town, \(25\%\) of the families own a phone and \(15\%\) own a car; \(65\%\) families own neither a phone nor a car and \(2,000\) families own both a car and a phone. Consider the following three statements \((A)\,\,\,5\%\) families own both a car and a phone
\((B)\,\,\,35\%\) families own either a car or a phone
\((C)\,\,\,40,000\) families live in the town
Then,
- A Only \((A)\) and \((C)\) are correct.
- B Only \((B)\) and \((C)\) are correct
- C All \((A),\) \((B)\) and \((C)\) are correct.
- D Only \((A)\) and \((B)\) are correct
Answer & Solution
Correct Answer
(C) All \((A),\) \((B)\) and \((C)\) are correct.
Step-by-step Solution
Detailed explanation
\(n(P)\, = \,25\,\% \) \(n(C)\, = \,15\,\% \) \(n(P'\, \cup \,C')\, = \,65\,\% \) \( \Rightarrow n(P \cup \,C')\, = \,65\,\% \) \(n(P \cup \,C)\, = \,35\,\% \) \(n(P \cap \,C)\, = \,n(P)\, + n(C)\, - \,n(P \cup \,C)\) \(25\, + \,15\, - 35\, = \,5\% \)…
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