Question

IN a group pf 400 people, 250 can speak hindi and 200 can speak english.How many people can speak both hindi and english, using venn diagram​

Answer 1

$\huge \rm {Answer:-}$

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$\sf \red {\underline{Given:}}$

★Group of people=400

$\colon \implies \bf {n(H\:∪\:E)=400}$

★No. of people who can speak Hindi(H)=250

$\colon \implies \bf {n(H)=250}$

★No. of people who can speak English(E)=200

$\colon \implies \bf {n(E)=200}$

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$\sf \blue {\underline{To\: Find:}}$

★No. of people who can speak both hindi and english=?

$\colon \implies \bf {n(H\:∩\:E)=?}$

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$\sf \pink {\underline{We\: know:}}$

$\colon \implies \bf {n(H\:∪\:E)=n(H)+n(E)-n(H\:∩\:E)}$

$\colon \implies \bf {400=250+200-n(H\:∩\:E)}$

$\colon \implies \bf {400=450-n(H\:∩\:E)}$

$\colon \implies \bf {n(H\:∩\:E)=450-400}$

$\colon \implies \bf \green{\fbox{n(H\:∩\:E)=50}}$

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$\sf \purple {\underline{Thenceforth,}}$

★No. of people who can speak both hindi and english= 50