A pendulum clock loses $12\;s$ a day if the temperature is $40 ^{\circ} C $ and gains $4s\;a$ day if the temperature is $20 ^{\circ}C$. The temperature at which the clock will show correct time, and the co-efficient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively :

Question

$\begin{array}{1 1} (1)25^{\circ}C ; \alpha = 1.85 \times 10^{-5}/^{\circ} C \\ (2)60^{\circ}C ; \alpha = 1.85 \times 10^{-4}/^{\circ} C \\ (3)30^{\circ}C ; \alpha = 1.85 \times 10^{-3}/^{\circ} C \\ (4)55^{\circ}C ; \alpha = 1.85 \times 10^{-2}/^{\circ} C \end{array} $