Question

The steam point and the ice point of a mercury thermometer are marked as ${80}^{\circ }$ and ${10}^{\circ }$. At what temperature on centigrade scale the reading of this thermometer will be ${59}^{\circ }$?

Answer 1

Let the relation between the thermometer reading and centigrade be
$y=ax+b$
given at $x=100,y=80$ and at $x=0,y=10$
$\therefore 80=100a+b,10=b\Rightarrow a=0.7$
Now, we have to find $x$ when $y=59$
$\therefore 59=0.7x+b\Rightarrow x=70$
$\therefore$ The answer is ${70}^{\circ }C$.