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

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Solution

Let E be the set of all students who know English and H be the set of all students who know Hindi.
Number of students who know Hindi $= n (H) = 100$
Number or students who know English $= n (E) = 50$
Number of students who know both Hindi and English $= n (H C a p E) = 25$
Since, each the students know Hindi or English

Number of students in group

$=$ Number of students who know Hindi or English
$= n (H \cup E)$

We know that $n (H \cup E) = n (H) + n (E) - n (H \cap E)$
$= 100 + 50 - 25$
$∴ n (H U E) = 125$

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

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