How does mixed damage types work?
 

Some of the units have do more then one type of damage with their main attack.

Let say unit doing 10-20 fire/physical damage hit my unit with 50% physical 0% fire resistance (let say unit have same defense as opponent has its attack and there are no other damage modifiers in play)

How much damage my unit take?

Which troop are you using, usually your unit will do 50% physical damage and full fire damage to enemy troop (~3-5 physical and 5-10 fire)