Question

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

Answer 1

Hint: To solve this kind of question we use a sets formula. Also use the set’s properties such as union, intersection of sets to find the total number of students in the group etc.

Complete step-by-step answer:
In this question given that,
 $ 100 $ students who know Hindi.
 $ 50 $ knows English.
 $ 25 $ knows both Hindi and English.
We have to find the total number of students in the group.
Let $ x $ be the set of all students in the group.
Let $ y $ be the set of students who know English.
Let $ z $ be the set of students who know Hindi.
let $ f $ be the set of students who know both Hindi and English.
According to the above condition,find
 $ \Rightarrow n(x) = n(z) + n(y) - n(f) $
 $ n(y) = 50 $
 $ n(z) = 100 $
 $ n(f) = 25 $
Put these value in the above condition,
 $ \Rightarrow n(x) = 100 + 50 - 25 $
On simplifying the above equation, we get,
 $ n(x) = 125 $
Hence,
The total number of students in the group is $ 125. $

Note: We have used a set formula $ n(A \cup B) = n(A) + n(B) - n(A \cap B) $ to solve the question.
Here, $ n(A \cup B) = $ Set of the total number of $ A $ and $ B. $
 $ n(A) = $ Set of the number of $ A. $