At what temperature do the Celsius and Fahrenheit readings have the same numerical value ?

Explanation

Let the two scales coincide at tempearture t
` ( C )/( 100 ) = ( F - 32)/( 180)`
`F = (9)/( 5) C + 32`
`t = (9)/( 5) t + 32`
`(9)/(5) t -t = - 32`
`0.8 t = - 32`
or `t = ( - 32)/( 0.8) = - 40^(@)C`
i.e., at `- 40^(@)C` the Celsius and Fahrenheit scales coincide.