Question

Out of 500 first year students, 260 passed in the first semester and 21 0 passed in the second semester. If 170 did not pass in either semester, how many passed in both semesters ?

• A. $30$
• B. $40$
• C. $70$
• D. $140$

Answer 1

Answer: (D)

$140$

Let A be the set of students who passed first semester so $n\left(A\right)=260$

and B be the set of students who passed second semester so $n\left(B\right)=210$.

Now $170$ did not passed any semester

So, $(500-170=330)$ students passed atleast one of the semesters

$\therefore n(A\cup B)=330$

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

$330=260+210-n(A\cap B)$

$n(A\cap B)=140$