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On a new temperature scale, the melting point of ice is 20 ${ }^{\circ} \mathrm{X}$ and the boiling point of water is $110^{\circ} \mathrm{X}$. A temperature of $40^{\circ} \mathrm{C}$ would be indicated on this new temperature scale as
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$56 ^\circ X$
$\begin{aligned} & \frac{\text { Reading on new scale -LFP }}{\text { UFP - LFP }}=\frac{\mathrm{C}-0}{100} \\ & \frac{\mathrm{z}^{\circ} \mathrm{X}-20^{\circ} \mathrm{X}}{110^{\circ} \mathrm{X}-20^{\circ} \mathrm{X}}=\frac{40-0}{100} \Rightarrow \mathrm{z}^{\circ} \mathrm{X}-20^{\circ} \mathrm{X} \\ & =\frac{40}{100} \times 90^{\circ} \mathrm{X}=36^{\circ} \mathrm{X} \\ & \therefore \text { Reading on new scale. } \\ & \mathrm{z}^{\circ} \mathrm{X}=36^{\circ} \mathrm{X}+20^{\circ} \mathrm{X}=56^{\circ} \mathrm{X}\end{aligned}$
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