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In a group of 500 students, there are 475 students who can speak Hindi and 200 can speak Bengali. What is the number of students who can speak Hindi only ?
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The correct answer is:
300
Total number of students $=500$ Let $\mathrm{H}$ be the set showing number of students who can speak Hindi $=475$ and $\mathrm{B}$ be the set showing number of students who can speak Ben gali $=200$ So, $\mathrm{n}(\mathrm{H})=475$ and $\mathrm{n}(\mathrm{B})=200$ and given that $\mathrm{n}(\mathrm{B} \cup$
$\mathrm{H})=500$
we have $n(B \cup H)=n(B)+n(H)-n(B \cap H)$
$\Rightarrow 500=200+475-n(B \cap H)$
$0, \mathrm{n}(\mathrm{B} \cap \mathrm{H})=175$
Hence, persons who speak Hindi only $=\mathrm{n}(\mathrm{H})-\mathrm{n}(\mathrm{B} \cap \mathrm{H})$
$=475-175=300$
$\mathrm{H})=500$
we have $n(B \cup H)=n(B)+n(H)-n(B \cap H)$
$\Rightarrow 500=200+475-n(B \cap H)$
$0, \mathrm{n}(\mathrm{B} \cap \mathrm{H})=175$
Hence, persons who speak Hindi only $=\mathrm{n}(\mathrm{H})-\mathrm{n}(\mathrm{B} \cap \mathrm{H})$
$=475-175=300$
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