Question

In a group of students, $75$ scored first class marks in Kannada, $70$ scored first class marks in Social science and $45$ scored first class in both the subjects. Find the number of students in the group.

Answer 1

Number of students who scored I class in Kannada, $n\left(K\right)=75$
Number of students who scored I class in Social science $n\left(S\right)=70$
Number of students who scored I class in both the subjects $n(K\cap S)=45$
Number of students $=n(K\cup S)=?$
$n(K\cup S)=n\left(K\right)+n\left(S\right)-n(K\cap S)$
$\therefore n(K\cup S)=75+70-45=145-45=100.$
so, there are 100 students in the group.
The above problem can also be solved using Venn diagram. Study the following Venn diagram. It has two intersecting circles, each representing a subject. The number of students in each group is calculated as shown.
The result is verified as follows:
Number of students in the group $=30+45+25=100$