Question

in a group of 50 people ,35 speak hindi ,25 speak both english and hindi and all the people speak at least one of two languages . then the number of people speak only english are : 20,15,30,40
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Answer 1

Answer:

15 people speak only english

Answer 2

$Given \: number \: of \: Hindi \: speaking \\people \: n(H) = 35$

$Let \: number \: of \: English \: speaking \\people \: n(E) = ?$

$Number \:of \: people \: who \:speak \\both \: languages \: n( H \cap E ) = 25$

$Total \: people \: in \: the \: group \: n( H \cup E)\\= 50$

$\boxed { \pink{ n(E) + n(H) = n(E\cup H) + n(E\cap H ) }}$

$\implies n(E) + 35 = 50 + 25$

$\implies n(E) = 75 - 35$

$= 40$

$Now , \red{ The \: number \: of \: people }\\\red{ who\: speak \: only \: English } \\= n(E) - n( H \cap E ) \\= 40 - 25 \\= 15$

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