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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, $$20 \leq x \leq 50$$
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