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In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?
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Verified Answer
Let $\mathrm{H}=$ Set of people who can speak Hindi and $\mathrm{E}=$ Set of people who can speak English.
Then, $n(H)=250 n(E)=200$
and $n(H \cup E)=400$
Now, $n(H \cup E)=n(H)+n(E)-n(H \cap E)$
$\Rightarrow 400=250+200-n(\mathrm{H} \cap \mathrm{E})$ $\Rightarrow n(H \cap E)=450-400=50$
Hence, 50 people can speak both Hindi and English.
Then, $n(H)=250 n(E)=200$
and $n(H \cup E)=400$
Now, $n(H \cup E)=n(H)+n(E)-n(H \cap E)$
$\Rightarrow 400=250+200-n(\mathrm{H} \cap \mathrm{E})$ $\Rightarrow n(H \cap E)=450-400=50$
Hence, 50 people can speak both Hindi and English.
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