Question

In a group of $500$ students, there are $475$ students who can speak Hindi and $200$ can speak Bengali. What is the number of students who can speak Hindi only?

• A. $275$
• B. $300$
• C. $325$
• D. $350$

Answer 1

The correct option is B

$300$

Explanation for the correct answer:

Find the number of students who can speak Hindi only.

Given,

$475$ students can speak Hindi.

$200$ students can speak Bengal.

We know that,

$X\left(A\cup B\right)=X\left(A\right)+X\left(B\right)-X\left(A\cap B\right)$

Let,

$X\left(A\right)$ be the students who speak Hindi , $X\left(B\right)$ be the students who speak Bengal and $X\left(A\cup B\right)$ be the total number of students.

So,

$X\left(A\right)=475,X\left(B\right)=200,X\left(A\cup B\right)=500$

Now,

$\begin{array}{rcl}X\left(A\cup B\right)& =& X\left(A\right)+X\left(B\right)-X\left(A\cap B\right)\\ 500& =& 475+200-X\left(A\cap B\right)\\ X\left(A\cap B\right)& =& 175\end{array}$

So the number of students who can speak Hindi only $=475-175=300$

Hence, the correct option is B.