Question

In a group of students, $100$ students know Hindi,$50$ know English and $25$ know both. Each of the students knows either Hindi or English. How many students are there in the group?

Answer 1

Find the number of students in the group.

Given: $\mathrm{n}\left(\mathrm{H}\right)=100,\mathrm{n}\left(\mathrm{E}\right)=50$ and $\mathrm{n}(\mathrm{H}\cap \mathrm{E})=25$

Let, $\mathrm{n}\left(\mathrm{H}\right)$ denote the number of students who can speak Hindi, $\mathrm{n}\left(\mathrm{E}\right)$ denote the number of students who can speak English, $\mathrm{n}(\mathrm{H}\cap \mathrm{E})$ denote the number of students who can speak both Hindi and English and $\mathrm{n}(\mathrm{H}\cup \mathrm{E})$ denote the total number of students in the group.

We know that,

$$\begin{gathered} \mathrm{n}(\mathrm{H}\cup \mathrm{E})=\mathrm{n}\left(\mathrm{H}\right)+\mathrm{n}\left(\mathrm{E}\right)-\mathrm{n}(\mathrm{H}\cap \mathrm{E}) \\ =100+50-25 \\ =150-25 \\ =125 \\ \therefore \mathrm{n}(\mathrm{H}\cup \mathrm{E})=125 \end{gathered}$$

Hence, there are $125$ students in the group.