What percentage of water is lost through the respiratory system?

It's about 10 to 20 percent

The normal daily input of water is about 2.5 L from beverages food, and metabolism. The normal daily output of 2.5 L consists of 1.8 L in urine, sweat, and feces, plus 0.7 L in insensible water loss. Insensible water loss is water that evaporates through the skin and from the respiratory tract. Insensible losses account for 0.7 L of water loss per day. The average human exhales an average of 0.35 L of water each day. This corresponds to about 14% of water lost through respiration.