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In a class consisting of $100$ students, $20$ know English and $20$ do not know Hindi and $10$ know neither English nor Hindi. The number of students knowing both Hindi and English is:

  1. $5$
  2. $10$
  3. $15$
  4. $20$
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According to the question

 $E+H=100$,

where;

 $E$ = number of students who can speak English,

$H$ = number of a student who can speak Hindi.

There are $10$ students who don’t speak any one of the languages.

$\therefore$ $H+E=90$

$n(E)=20,n(H)=80,n(H\cup E=90)$

$\because$ $n(H\cup E)=n(E)+n(H)-n(H\cap E)$

$\implies$ $90=20+80-n(H\cap E)$

$\implies$ $n(H\cap E)=10$

The number of students knowing both Hindi and English is $10$
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