Question

Temperature at which both the Celsius and Fahrenheit scales show the same reading?

• A. $40\text{K}$
• B. $100{}^o\text{F}$
• C. $-40{}^o\text{C}$
• D. $-100{}^o\text{C}$

Answer 1

The correct option is C $-40{}^o\text{C}$

The formulae for conversion between Celsius and Fahrenheit scales are:
${}^{o}C={(}^{o}F-32)\times \frac{5}{9}$
let ${}^{o}C={}^{o}F$
${}^{o}C={(}^{o}C-32)\times \frac{5}{9}$
Simplifying the the equation,
${}^{o}C-32={}^{o}C\times \frac{9}{5}{}^{}{}^{o}C=-32\times \frac{5}{4}=-40$
So, the temperature at which both the Celsius and Fahrenheit scales show the same reading is $-40{}^{o}C$