From principle of thermometry,

$\frac{T-T_{\mathrm{LFP}}}{T_{\mathrm{UFP}}-T_{\mathrm{LFP}}}=\mathrm{a}$ constant for every

thermometric scale.

Now, for any temperature $L$ on a thermometer designed with given liquid and equivalent temperature $C$ on centigrade scale, we have

${\left(\frac{L-T_{\mathrm{LF}}}{T_{\mathrm{UFP}}-T_{\mathrm{LFP}}}\right)}_{\text{Liquid based scale }}={\left(\frac{C-T_{\mathrm{LFP}}}{T_{\mathrm{UFP}}-T_{\mathrm{LFP}}}\right)}_{\text{Centigrade Scale }}$

$\Rightarrow \frac{L-(-50)}{150-(-50)}=\frac{C-0}{100-0}$

Now at $0°L,$ centigrade scale reading will be

$0+50=2 C$ or $C=\frac{50}{2}=25°L$

and at $100°L$, centigrade scale reading will be

$100+50=2 C$ or $C=\frac{150}{2}=75°L$