In a class of $150$ students, $70$ passed in mathematics, $60$ students passed in statistics and $20$ in both subjects. Then the number of students who failed in both subjects is:

Let $M$ be the set of students who passed in mathematics and $S$ be the set of students who passed in statistics.
Given:
Total students, $n(U)=150$
$n(M)=70$
$n(S)=60$
$n(M\cap S)=20$

The total number of students who passed in at least one subject is given by:

$$n(M\cup S)=n(M)+n(S)-n(M\cap S)$$

$$n(M\cup S)=70+60-20=110$$

The number of students who failed in both subjects is:

$$\text{Failed students}=n(U)-n(M\cup S)=150-110=40$$