Question

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

• A. $5$
• B. $10$
• C. $15$
• D. $20$

Answer 1

Given total number of students in a class is $n\left(U\right)=100$
Number of students knows English is $n\left(E\right)=20$
Number of students do not know Hindi is $20$
So, the number students knows Hindi is $n\left(H\right)=100-20=80$

Number of students who have studied neither Hindi nor English is $=10$
So, the number of students who knows either English or Hindi is $n(E\cup H)=n\left(U\right)-$ n(students who studied neither) $=100-10=90$

Since, we have $n(E\cup H)=n\left(E\right)+n\left(H\right)-n(E\cap H)$
$90=20+80-n(E\cap H)$
$\therefore n(E\cap H)=10$
Hence, the number of students who knows both English and Hindi is $10$
Thus, the correct option is B ($10$).