Let the number be  $\text{'}x\text{'}$

The number $\text{'}x\text{'}$ multiplied by $\text{'}4\text{'}$ and  $\text{'}5\text{'}$ is added to the product  $=4x+5$

If  $4x+5$ is divided by  $11,\text{\hspace{0.17em}\hspace{0.17em}it\hspace{0.17em}becomes\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\frac{4x+5}{11}$

As per the problem this result is equal to $\text{'}7\text{'}$

$\frac{4x+5}{11}=\frac{7}{1}$

By cross multiplication

$\begin{array}{l}4x+5=7\left(11\right)\\ 4x+5=77\\ 4x=77-5\\ 4x=72\\ x=\frac{72}{4}\\ x=18\end{array}$

 the required number  $\left(x\right)=18$