4. Let the carrying capacity of the truck be $a$ tons, and for transporting 60 tons of sand, $n$ trips were required. Then there are two possible situations:
a) $n-1$ full trucks and no more than half a truck: then to transport 120 tons, $2(n-1)+1=2n-1$ trips will be needed. According to the condition, $2n-1-n=5$, so $n=6$. This situation is realized if $5a<60$ and $5.5a \geqslant 60$, that is, $\left[10 \frac{10}{11} ; 12\right)$.

b) $n-1$ full trucks and more than half a truck: then to transport 120 tons, $2(n-1)+2=2n$ trips will be needed. According to the condition, $2n-n=5$, so $n=5$. Then: $4.5a<60$ and $5a \geqslant 60$, that is, $\left[12 ; 13 \frac{1}{3}\right)$.
Answer: $\left[10 \frac{10}{11} ; 13 \frac{1}{3}\right)$ tons.

Answer to the variant: $5-2:\left[9 \frac{1}{11} ; 11 \frac{1}{9}\right)$ tons.