In a factory $70\%$of the workers like oranges and $64\%$ like apples. If $x\%$ like both oranges and apples, then

Let the total number of workers be$100. A,$ the set of workers who like oranges and $B$, the set of workers who like apples.

So   $n\left(A\right)=70,n\left(B\right)=64,n(A\cap B)=x$

Also $\begin{array}{l}n(A\cup B)\le 100\\ \Rightarrow n\left(A\right)+n\left(B\right)-n(A\cap B)\le 100\\ \Rightarrow 70+64-x\le 100\Rightarrow x\ge 34\end{array}$

Since $n(A\cap B)\le n\left(B\right)\Rightarrow x\le 64$

Hence $34\le x\le 64$