Sometimes I carry only 2 sets of clothes with me. One that is currently on me and the other that is in the bag. So at times I actually have to wash the clothes in the hotel. You can actually buy this handy laundry washing stuff from travel stores but if not. You can also try to just use water / hot water or soap to wash your clothes.

How long does it take to dry the shirt? (Excluding hair dryer and also if you have a balcony to dry them outside)
It takes less than a day in the hotel room. Checked in yesterday at the hotel at around 6. So finish washing around 7. By around next day morning 6 or so it was dry. I usually wash the shirt with soap leave it for 5 mins. Then wash it again to get the soap out. Squeeze it dry. Leave it hanging in the bathroom for a while. Squeeze it again. Put it in the room hanging to dry.

How long does it take for the pants to dry? (Mine is actually kinda of like cargo pants?)
More than a day. Probably 2 days. Started out at 7pm yesterday and today around 8am still not dry yet. (14-06-19 update) took out my pants to dry again. Can say by the second day they are about dry already.