A fort had provisions for 150 men for 45 days. After 10 days, 25 men left. How long will the food last at the same rate?

To solve this problem, we need to calculate the rate at which the provisions are being consumed and then determine how long they will last with the reduced number of men.

Step 1: Calculate the rate of consumption The provisions are meant to last for 150 men for 45 days. This means that the total amount of provisions is enough to feed 150 men for 45 days.

To find the rate of consumption, we divide the total provisions by the number of days: Rate of consumption = Total provisions / Number of days Rate of consumption = 150 men * 45 days = 6750 man-days

Step 2: Adjust for the reduced number of men After 10 days, 25 men left the fort. This means that there are now 150 - 25 = 125 men remaining.

To find the new rate of consumption, we multiply the rate of consumption by the number of men remaining: New rate of consumption = Rate of consumption * Number of men remaining New rate of consumption = 6750 man-days * 125 men = 843,750 man-days

Step 3: Calculate how long the provisions will last To find out how long the provisions will last at the new rate of consumption, we divide the total provisions by the new rate of consumption: Number of days = Total provisions / New rate of consumption Number of days = 6750 man-days / 843,750 man-days = 0.008 days

Therefore, the provisions will last approximately 0.008 days at the same rate.