At what temperature do the Fahrenheit scale and Kelvin scale coincide?

Solution

The relation between Fahrenheit and Kelvin is given as,
$space fraction numerator straight F minus 32 over denominator 180 end fraction equals fraction numerator straight K minus 273 over denominator 100 end fraction$
Let at temperature T, Fahrenheit scale and Kelvin scale readings coincide.
∴ $space space space fraction numerator straight T minus 32 over denominator 180 end fraction equals fraction numerator straight T minus 273 over denominator 100 end fraction$
$rightwards double arrow$ $5 straight T minus 160 space equals space 9 straight T minus 2457$
$rightwards double arrow$ $4 straight T space equals space 2297$
Thus, $space straight T equals 574.25 degree$
So at this temperature, the Fahrenheit and the kelvin scale coincide.