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?
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?

Solution:

Let’s suppose that,

The set of all students in the group be U

The set of students who know English be E

$\therefore \mathrm{H} \cup \mathrm{E}=\mathrm{U}$

Provided that,

$n(H)=100$ = Number of students who know Hindi

$n(E)=50$ = Number of students who knew English,

$n(H \cap E)=25$ = Number of students who know both,

We need to find the total number of students in the group i.e. $n(U)$

$\therefore$ As per the question,

$n\text{ }\left( U \right)\text{ }=\text{ }n\left( H \right)\text{ }+\text{ }n\left( E \right)-n(H\cap E)$

$=\text{ }100\text{ }+\text{ }50-25$

$= 125$

$\therefore$ $125$ is the total number of students in the group students.