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?
Let $U$ be the set of all students in the group.
Let $E$ be the set of all students who know English.
Let $H$ be the set of all students who know Hindi.
$\therefore H \cup E=U$
Accordingly, $n(H)=100$ and $n(E)=50$
$n(H \cap E)=25$
$n(U)=n(H)+n(E)-n(H \cap E)$
$=100+50-25$
$=125$
Hence, there are $125$ students in the group.
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- [JEE MAIN 2021]