n(A) = 30, n(B) = 40 and n( AUB ) = 45.

Apply counting formula:

45 = 30 + 40  − n( A∩B )       (Substitute the values)

45 = 70  − n( A∩B )

n( A∩B ) = 70 − 45

n( A∩B ) = 25

n( A∩B ) = 25