Question

In a class 20 opted for Physics, 17 for maths, 5 for both and 10 for other subjects. The class contains how many students
a. 35
b. 42
c. 52
d. 60

Answer 1

Hint: Here in this question, we have to find how many students are there in the class. The question involves the opted students of particular subjects namely physics and maths. We use the concept of sets and simplify this. The obtained the required solution for the question. We can also solve this by using the Venn diagram.

Complete step by step solution:
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.
Now consider the given question, they have given 20 students who have opted physics and 17 have opted maths. The 5 students have opted both physics and maths And 10 other students have opted other subjects.
The number of the students opted Physics is given by \[n(P) = 20\]
The number of the students opted Maths is given by \[n(M) = 17\]
The number of students have opted both maths and physics is given by \[n(P \cap M) = 5\]
Therefore the total number of students have opted the subjects Maths and Physics is given by \[n(P \cup M) = ?\]
We can find this by using the formula
\[n(P \cup M) = n(P) + n(M) - n(P \cap M)\]
On substituting these values in the formula we have
\[ \Rightarrow n(P \cup M) = 20 + 17 - 5\]
On adding 20 and 17 we have
\[ \Rightarrow n(P \cup M) = 37 - 5\]
On subtracting 5 from 37 we have
\[ \Rightarrow n(P \cup M) = 32\]
We have 10 other students also
Therefore the total number of students are \[32 + 10\]
\[ \Rightarrow 42\]
Therefore the class contains 42 students.
Option B is the correct one.
So, the correct answer is “Option B”.

Note: The union formula in the set theory is given by \[n(A \cup B) = n(A) + n(B) - n(A \cap B)\], in general. Where A and B are two sets. We can write the Venn diagram for this concept or question. While simplifying this question we use the simple arithmetic operations like addition and subtraction.