Question

There are 60 students in a class who speak at least one language Hindi or English. If 45 students speak Hindi and 30 speak English, then the number of students who speak only Hindi-
A. 25
B. 19
C. 20
D. 30

Answer 1

Hint: First we will first subtract the number of students who speak at least one language Hindi or English from the sum of students who speak Hindi and English to find the number of students who speak both languages and then subtract the obtained difference number from the number of students who speak Hindi to find the students who only speak Hindi.

Complete step by step answer:

We are given that there are 60 students in a class who speak at least one language Hindi or English. If 45 students speak Hindi and 30 speak English.
Let us assume that the number of students who speak only Hindi is \[x\].
Subtracting the number of students who speak at least one language Hindi or English from the sum of students who speak Hindi and English to find the number of students who speak both languages, we get
\[
   \Rightarrow \left( {45 + 30} \right) - 60 \\
   \Rightarrow 75 - 60 \\
   \Rightarrow 15 \\
 \]
As the above number contains students who speak both languages so we will subtract the above number from the number of students who speak Hindi to find the value of \[x\], we get
\[
   \Rightarrow x = 45 - 15 \\
   \Rightarrow x = 30 \\
 \]

Thus, the required numbers of students who only speak Hindi are 30.
Hence, option D is correct.


Note: In solving these types of questions, students can also solve this question by making the Venn diagram, which is more understandable but less presentable. Since are given that there are 60 students in a class who speak at least one language Hindi or English. Then draw the Venn diagram for the students who speak at least one of the languages.

 Shading the region when the 45 students speak Hindi in the Venn diagram, we get

We will now shade the region when 30 students speak English, we get

From the above diagrams, we get that the intersection of Hindi and English languages will be the required answer, so we have

So, we follow the above method instead of making a diagram for more presentations.