If intensity is increased by factors of 20 .Then by how many decibels the sound level will increase ?

Let I and I' be the old and new intensity of sound. Then, according to question
$$\begin{gathered} I\text{'}=20I \\ \Rightarrow \frac{I\text{'}}{I}=20 \end{gathered}$$

We know that
$\beta =10{\log }_e\left(\frac{I}{I_0}\right) (\mathrm{in} \mathrm{dB})$
Then change in sound level can be given as
$$\begin{gathered} \Delta \beta ={\beta }_2-{\beta }_1=10{\log }_e\left(\frac{I\text{'}}{I_0}\right)-10{\log }_e\left(\frac{I}{I_0}\right)=10{\log }_e\left(\frac{I\text{'}}{I}\right) \\ \Rightarrow \Delta \beta =10{\log }_e\left(20\right)\simeq 10\times 3=30 \mathrm{dB} \end{gathered}$$