At what temperature, if any, do the following pairs of readings give the same reading on Fahrenheit and Kelvin scales?

If the temperature is q at which the reading of two scales is same, then $\frac{\mathrm{\theta }-32}{180}=\frac{\mathrm{\theta }-273.15}{100}\text{ i.e. },\mathrm{\theta }=574{.6}^{\circ }$

i. e. , reading on Fahrenheit and Kelvin scales coincides at 574.6°.