Option D: 10 days
Let's break down the problem step by step:
     1. Initial Food Supply: The garrison initially has food for 1000 soldiers for one month (30 days). This means the total food supply is equivalent to 1000 soldiers × 30 days = 30,000 soldier-days of food.
     2. Food Consumption in the First 10 Days: For the first 10 days, there are 1000 soldiers consuming the food. Therefore, the food consumed in these 10 days is 1000 soldiers × 10 days = 10,000 soldier-days of food.
     3. Remaining Food: After 10 days, the remaining food is 30,000 soldier-days - 10,000 soldier-days = 20,000 soldier-days of food.
     4. Increased Number of Soldiers: After 10 days, 1000 more soldiers join, making a total of 2000 soldiers in the garrison.
     5. Calculating Remaining Days: With 2000 soldiers now, we need to determine how long the remaining 20,000 soldier-days of food will last.
            ○ The number of days the remaining food will last is calculated by dividing the remaining soldier-days of food by the number of soldiers:
        \[
        \text{Remaining Days} = \frac{\text{Remaining Soldier-Days of Food}}{\text{Number of Soldiers}} = \frac{20,000}{2000} = 10 \text{ days}
        \]
     Therefore, the soldiers would be able to carry on with the remaining food for 10 days.