9. Five marks exercise problems VII

1. In an examination $50\%$ of the students passed in Mathematics and $70\%$ of students
passed in Science while $10\%$ students failed in both subjects. $300$  students passed in
atleast one subject. Find the total number of students who appeared in the examination, if they took examination in only two subjects.

 

The total number of students who appeared in the examination $=$

 

 

2. $A$ and $B$ are two sets such that $n(A – B) = 32 + x$, $n(B – A) = 5x$ and $n(A \cap B) = x$. Illustrate the information by means of a Venn diagram. Given that $n(A) = n(B)$, calculate the value of $x$.

 

$x =$