CAT 2019 Shift 2 Paper

Both the sequences are in arithmetic progression.
The common difference $\left({\mathit{d}}_1\right)$ for the first sequence $=4$
The common difference $\left({\mathit{d}}_2\right)$ for the first sequence $=5$
The first term common is $19.$
The common terms will also be in arithmetic progression with common difference $\mathit{L}\mathit{C}\mathit{M}\left({\mathit{d}}_1,{\mathit{d}}_2\right)=\mathit{L}\mathit{C}\mathit{M}\left(4,5\right)=20$
Let there be 'n' terms in this sequence, then the last term would be $\le 415$
i.e. $\mathit{a}+\left(\mathit{n}-1\right)\mathit{d}\le 415$
$\Rightarrow 19+\left(\mathit{n}-1\right)\times 20\le 415$
$\Rightarrow \left(\mathit{n}-1\right)\times 20\le 415-19$
$\Rightarrow \left(\mathit{n}-1\right)\times 20\le 396$
$\Rightarrow \left(\mathit{n}-1\right)=\left[\frac{396}{20}\right]$ where [ n] is the greatest integer
$\Rightarrow \left(\mathit{n}-1\right)=19$
$\Rightarrow \mathit{n}=20$