The total amount of rice that the military unit needs to prepare is:

30 people x 15 days = 450 person-days

This means that the unit needs to provide enough rice for 450 person-days of meals.

Since the amount of food each person eats per day is the same, we can say that the daily rice consumption of the entire unit is:

Total rice consumption / Total number of days = 450 person-days / 15 days = 30 person-days per day

This means that the unit consumes a total of 30 person-days worth of rice per day.

After eating for 3 days, there are 27 people left in the unit, and they need to eat for 12 more days (15 days - 3 days). The total number of person-days they need for these 12 days is:

27 people x 12 days = 324 person-days

Since the remaining rice needs to last for 324 person-days, we can calculate the number of days it will last by dividing the remaining rice by the daily rice consumption:

Remaining rice / Daily rice consumption = 324 person-days / 30 person-days per day = 10.8 days

Therefore, the remaining rice will last for approximately 10.8 days, or about 11 days if rounded up to the nearest whole number. So the unit will eat the remaining rice in 11 days approximately.