#### Answer

$25$

#### Work Step by Step

Given:
$n(A)=30, n(B)= 40 , n(A\cup B) = 45$.
Use the formula $n(A\cup B) = n(A) + n(B) - n(A \cap B)$ to obtain:
$n(A\cup B) = n(A) + n(B) - n(A \cap B)
\\45 = 30+40 -n(A\cap B)
\\45=70-n(A \cap B)
\\n(A \cap B) = 70-45
\\n(A \cap B) = 25$
Thus, $n(A \cap B)=25$.