Correct Option
The initial food supply was sufficient for 1000 soldiers for 30 days. After 10 days, 1000 soldiers consumed food for 10 days.
The remaining food supply is equivalent to what 1000 soldiers would consume in (30 - 10) = 20 days. This represents a total of 1000 soldiers * 20 days = 20,000 soldier-days of food.
Subsequently, 1000 additional soldiers joined, increasing the total number of soldiers to 1000 + 1000 = 2000 soldiers.
To determine how long the remaining food will last for 2000 soldiers, divide the total soldier-days of food by the new number of soldiers: 20,000 soldier-days / 2000 soldiers = 10 days.
Incorrect Options
The other options are incorrect as they do not reflect the accurate calculation based on the change in the number of soldiers after 10 days.
- Option 1 (25 days) and Option 3 (15 days) result from miscalculations regarding the remaining food supply or the increased number of soldiers.
- Option 2 (20 days) represents the duration the food would have lasted for the original 1000 soldiers, without accounting for the additional 1000 soldiers who joined the garrison.