Question

In a School 150 students passed $X$ standard Examination. 95 students applied for Group $I$ and 82 students applied for Group $II$ in the Higher secondary course. If 20 students applied neither of the two, how many students applied for both groups?

Answer 1

Given : the number of students who passed $X$ standard examination$=150$

No of students who applied for Group I $=n\left(A\right)=95$

No of students who applied for Group II $=n\left(B\right)=82$

No of students who applied in neither of the groups $=20$

$\therefore$ no of students who applied in either of the groups $=n(A\cup B)=150-20=130$

No of students who applied in both the groups $=n(A\cap B))$

Now, $n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$

$=95+82-130=47$