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  4. The temperature at which centigrade and Fahrenheit scales give the same reading, is

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Q. The temperature at which centigrade and Fahrenheit scales give the same reading, is

Thermal Properties of Matter

Solution:

Using relation,
$\frac{F-32}{180}=\frac{C}{100}$
If $F=C=x$, then substituting value in Eq. (i), we get
$\Rightarrow \frac{x-32}{180}=\frac{x}{100}$
$ \Rightarrow \frac{x}{5}=\frac{x-32}{9}$
$\Rightarrow 9 x=5 x-160$
$ \Rightarrow 160=-4 x$
$\therefore x=-40^{\circ}$
This is the required temperature at which centigrade and Fahrenheit scale give same reading.