\(\left(x\times1\right)+\left(x\times2\right)+\left(x\times3\right)+....+\left(x\times10\right)=240\)
\(\left(x\times x\times x\times....\times x\right)\times\left(1+2+3+...+10\right)=240\)
\(1x\times\frac{\left(10+1\right).10}{2}=240\)
\(1x\times55=240\)
\(1x=240\div55\)
\(1x=\frac{48}{11}\)
\(\Rightarrow x=\frac{48}{11}\)