1 vote

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:

- $5$
- $10$
- $15$
- $20$

0 votes

$\textrm{According to the question $E+H=100$,}$

$\textrm{where E=number of students who can speak English, H=number of a student who can speak Hindi.}$

$\textrm{there are 10 students who don’t speak any one of the languages.}$

$\therefore$ $H+E=90$

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

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

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

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

$\textrm{The number of students knowing both Hindi and English is 10}$

$\textrm{where E=number of students who can speak English, H=number of a student who can speak Hindi.}$

$\textrm{there are 10 students who don’t speak any one of the languages.}$

$\therefore$ $H+E=90$

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

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

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

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

$\textrm{The number of students knowing both Hindi and English is 10}$