Question

There are $60$ students in a class. Every student learns at least one of the subjects Kannada or English. $45$ students offer Kannada and $30$ English. How many students offer both the subjects? Draw Venn diagram.

Answer 1

Number of students in the class $=n(K\cup E)=60$
Number of students who offer Kannada$=n\left(K\right)=45$
Number of students who offer English $=n\left(E\right)=30$
Number of students who offer both the subjects $n(K\cap E)$
$n(K\cap E)=n\left(K\right)+n\left(E\right)-n(K\cup E)$
$45+30-60$
$=75-60$
$n(K\cap E)=15$
$\therefore$ Number of students who offer both the subjects$=n(K\cap E)=15$