Why charging time is same and discharge time is different for two inputs in dual slope integrating ADC?
During the integration time you charge a capacitor with a current proportional to the input voltage.  The final voltage on the cap is proportional to the input voltage.

During the de-integrate time you discharge a capacitor with a known fixed current.  Since the initial voltage was proportional to the input voltage the time it will take to decay to zero is also proportional to the input voltage.

So all you need to do to measure the input is time how long it takes to discharge the capacitance.

There are several other ways to design an ADC but this is a fairly simple method to implement.