Answer:
It would take 10 days to completely empty the rain gauge.
Explanation:
Initial reading of rain gauge = 10 inches
Every day rain evaporated by 2 inches but 1 more inch of rain was added.
In effect, only one inch of rain water evaporated that is everyday level decreased with 1 inch.
After the end of day 1 , the reading would show 9 inches and 8 inches at the end of day 2 and similarly reading decreases linearly.
Since the reading should decrease by 10 inches it would take 10 days to completely empty the rain gauge.