Question

There are $600$ students in the school. If $400$ of them can speak Telugu, and $300$ can speak Hindi, then the number of students who can speak both Telugu and Hindi is:

• A. $100$
• B. $200$
• C. $300$
• D. $400$

Answer 1

The correct option is A

$100$

Explanation for the correct answer

Let $\mathrm{A}=$set of students speaks Telugu and $\mathrm{B}=$ set of students speak Hindi.

Given: $\mathrm{n}\left(\mathrm{A}\cup \mathrm{B}\right)=600$

$$\begin{gathered} \mathrm{n}\left(\mathrm{A}\right)=400 \\ \mathrm{n}\left(\mathrm{B}\right)=300 \\ \Rightarrow \mathrm{n}(\mathrm{A}\cup \mathrm{B})=\mathrm{n}\left(\mathrm{A}\right)+\mathrm{n}\left(\mathrm{B}\right)-\mathrm{n}\left(\mathrm{A}\cap \mathrm{B}\right) \\ \Rightarrow 600=400+300-\mathrm{n}\left(\mathrm{A}\cap \mathrm{B}\right) \\ \Rightarrow \mathrm{n}\left(\mathrm{A}\cap \mathrm{B}\right)=700-600 \\ \Rightarrow \mathrm{n}\left(\mathrm{A}\cap \mathrm{B}\right)=100 \end{gathered}$$

$\mathrm{n}\left(\mathrm{A}\cap \mathrm{B}\right)=100$, is the number of students who speak Telugu and Hindi both.

Hence option (A), $100$ is the correct answer.