In a school 70% of the boys like cricket and 50% like football. If x% like both Cricket and Football, then

Let the total number of boys in the class be 100.

so, number of boys who like cricket = 70

similarly, number of boys who like football = 50

also, number of boys who like both cricket and football = $$x$$

also, let the number of students who like none of the sports be $$n$$

So, we can make a Venn diagram like:

So, $$\left(70-x\right)+x+\left(50-x\right)+n=100$$

or, $$x=n+20$$

Now, the minimum value of $$n$$ can be zero

So, minimum value of $$x$$ is 20

Also, $$50-x\ge0$$,or, $$x\le50$$

So, the maximum value of $$x$$ can be 50

So, $$20 \leq x \leq 50$$