A clock with a metallic pendulum gains 5s in a day at 15°C and loses 10s in a day at 30°C. Find the temperature at which the clock will read correct time.

Let L be the length and the temperature coefficient of linear expansion of pendulum clock. 
If the temperature of the clock is increased or decreased by θ, the length of the pendulum will increase or decrease by L . And the clock runs slow or fast.
Let the clock keep correct time when the length is L and temperature is t°C.
We know time period of the pendulum is given by, 
                         
The time period of oscillation of pendulum when the temperature is changed by θ is, 

 
The change in time period of oscillation of pendulum when the temperature is changed by θ is, 
 
The change in the time in a day, 
                 
where,  is the duration of the day. 
At  the gain is 5s.
Therefore,
                              ...(1) 
At  the loss is 10s.
Therefore,
                         ...(2) 
From (1) and (2), we get 
 , is the temperature at which the clock will read correct time.