Coincidence of Centigrade and Fahrenheit

The reading of Centigrade thermometer coincides with that of Fahrenheit thermometer in a liquid. The temperature of the liquid is:

\(- 40^\circ\text{C}\)

\(313^\circ\text{C}\)

\(0^\circ\text{C}\)

\(100^\circ\text{C}\)

Using the relation \(\frac{C}{5} = \frac{F - 32}{9}\), let \(C = F = x\). This gives \(\frac{x}{5} = \frac{x - 32}{9} ⇒ 9x = 5x - 160 ⇒ x = -40\).