Final answer:
The remaining food will last for approximately 48.6 days.
Step-by-step explanation:
To find the number of days for which the remaining food will last, we can first calculate how much food was available originally and then determine how long it will last with the increased number of men.
Initially, the garrison had provisions for 1000 men for 70 days. This means that the total amount of food available was enough to feed 1000 men for 70 days, or 70,000 units of food (1000 men x 70 days).
After 25 days, 200 more men join the garrison, bringing the total number of men to 1200. To find how long the remaining food will last, we divide the total amount of food by the increased number of men:
Remaining food = 70,000 units of food / 1200 men = 58.33 units of food per man
To find the number of days the remaining food will last, we divide the remaining food by the number of men:
Number of days = Remaining food / Number of men = 58.33 units of food per man / 1200 men = 0.0486 days per man
Multiplying the result by the original number of men, we get:
Number of days = 0.0486 days per man x 1000 men = 48.6 days
Therefore, the remaining food will last for approximately 48.6 days.