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A thermometer graduated according to a linear scale reads a value $x_{0}$ when in contact with boiling water, and $x_{0} / 3$ when in contact with ice. What is the temperature of an object in ${ }^{\circ} \mathrm{C}$, if this thermometer in the contact with the object reads $x_{0} / 2 ?$
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The correct answer is:
25
Let required temperature $=\mathrm{T}^{\circ} \mathrm{C}$
$\Rightarrow \mathrm{T}^{\circ} \mathrm{C}=\frac{\mathrm{x}_{0}}{2}-\frac{\mathrm{x}_{0}}{3}=\frac{\mathrm{x}_{0}}{6}$
$\&\left(\mathrm{x}_{0}-\frac{\mathrm{x}_{0}}{3}\right)=\left(100-0^{\circ} \mathrm{C}\right)$
$\Rightarrow \frac{2 \mathrm{x}_{0}}{3}=100 \Rightarrow \mathrm{x}_{0}=\frac{300}{2}$
$\Rightarrow \mathrm{T}^{\circ} \mathrm{C}=\frac{\mathrm{x}_{0}}{6}=\frac{150}{6}=25^{\circ} \mathrm{C}$
$\Rightarrow \mathrm{T}^{\circ} \mathrm{C}=\frac{\mathrm{x}_{0}}{2}-\frac{\mathrm{x}_{0}}{3}=\frac{\mathrm{x}_{0}}{6}$
$\&\left(\mathrm{x}_{0}-\frac{\mathrm{x}_{0}}{3}\right)=\left(100-0^{\circ} \mathrm{C}\right)$
$\Rightarrow \frac{2 \mathrm{x}_{0}}{3}=100 \Rightarrow \mathrm{x}_{0}=\frac{300}{2}$
$\Rightarrow \mathrm{T}^{\circ} \mathrm{C}=\frac{\mathrm{x}_{0}}{6}=\frac{150}{6}=25^{\circ} \mathrm{C}$
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