Question

A thermometer graduated according to linear scale reads a value $t$ when in contact with boiling water and $\frac{t}{4}$ when kept in contact with ice. When the thermometer is in contact with an object it reads $\frac{t}{3}$. What is the temperature of the object in ${ }^{\circ} C ?$

Answer 1

(Boiling point of water) - (ice point of water) $= 100^{\circ} C$
$\therefore \left( t -\frac{ t }{4}\right)=100{ }^{\circ} C $
$\therefore \frac{3 t }{4}=100 $
$\therefore t =\left(\frac{400}{3}\right){ }^{\circ} C$ ... (i)
Let, $T$ be the temperature of the object in ${ }^{\circ} C$.
$\therefore \left(\frac{ t }{3}-\frac{ t }{4}\right)=( T -0) $
$\therefore \frac{ t }{12}= T $
$\therefore \frac{400}{3 \times 12}= T$ .... [From (i)]
$\therefore T =\frac{100}{9}=11.11^{\circ} C$