Question

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

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

Answer 1

Answer: (C)

$-{40}^o$C

The relation between $°C$ and $°F$ is

$°F=\frac{9}{5}\left(°C\right)+32$

when $°F=°C$

$\therefore °C=\frac{9}{5}°C+32$

$\therefore °C-\frac{9}{5}°C=32$

$\therefore -\frac{4}{5}°C=32$

$\therefore °C=-40°C$

$\therefore T=-40℃$

$\therefore$ At $-40℃$, both the celcius and Fahrenheit scales show the same reading.