Question

In a group of $400$ people, $250$ can speak Hindi and $200$ can speak English. How many people can speak both Hindi and English?

Answer 1

Find the number of people that can speak both Hindi and English.

Given: $\mathrm{n}\left(\mathrm{H}\right)=250,\mathrm{n}\left(\mathrm{E}\right)=200$ and the total number of people $\mathrm{n}(\mathrm{H}\cup \mathrm{E})=400$

Let, $\mathrm{n}\left(\mathrm{H}\right)$ denote the number of people who can speak Hindi , $\mathrm{n}\left(\mathrm{E}\right)$ denote the number of people who can speak English and $\text{n(H∩E)}$ denote the number of people who can speak both Hindi and English.

We know that,

$$\begin{gathered} \mathrm{n}(\mathrm{H}\cap \mathrm{E})=\mathrm{n}\left(\mathrm{H}\right)+\mathrm{n}\left(\mathrm{E}\right)-\mathrm{n}(\mathrm{H}\cup \mathrm{E}) \\ =250+200-400 \\ =450-400 \\ =50 \\ \therefore \mathrm{n}(\mathrm{H}\cap \mathrm{E})=50 \end{gathered}$$

Hence, $50$ people can speak both Hindi and English.