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:

The correct option is B. $10$

From question,

Total number of students, $n\left(U\right)=100$
Number of students who know English, $n\left(E\right)=20$
Number of students who do not know Hindi $n(H{)}^{\prime }=20$
Number of student whose does not know either language $n(E\cap H{)}^{\prime }=10$

Number of students who know Hindi,
$n\left(H\right)=n\left(U\right)-n(H{)}^{\prime }=100-20=80$

Number of students who knows any or both of the language,

$n(E\cup H)=n\left(U\right)-n(E\cap H{)}^{\prime }=100-10=90$

By set theory,

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

$\Rightarrow 90=20+80-n(E\cap H)$
$\Rightarrow n(E\cap H)=100-90=10$
Hence, $10$ students know both of the languages.