JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Heat & Thermodynamics

The two scales share their lower and upper fixed points, so equal fractions of the interval between those points read the same temperature. Scale P runs from $30^{\circ }$ to $180^{\circ }$, a span of $150$ divisions, while scale Q runs from $0^{\circ }$ to $100^{\circ }$, a span of $100$ divisions. Equating the fractional rise above each lower point gives $\frac{t_P-30}{150}=\frac{t_Q}{100}$, which rearranges to the conversion $\frac{t_Q}{100}=\frac{t_P-30}{150}$.