Sound level $\beta$ is generally expressed (in decibel) as,

$\beta=10( dB ) \cdot \log _{10}\left(\frac{I}{I_0}\right)$

where, $\quad I_0=$ reference intensity $=10^{-12} \,W / m ^2$.

Now, let intensity is initially $I$, then sound level is

$\beta_1=10 \log _{10}\left(\frac{I}{I_{ 0 }}\right)$

When intensity increases by $100$ times, sound level will be

$\beta_2 =10 \log _{10}\left(\frac{100 I}{I_{0}}\right)$

$=10\left(\log _{10} 100+\log _{10}\left(\frac{I}{I_0}\right)\right)$

$\Rightarrow \beta_2=10 \log _{10} 100+\beta_1$

$\Rightarrow \beta_2-\beta_1=10 \times 2=20 \,dB$

So, sound level increases by $20 \,dB$.