Analysis:

To find out how long the remaining provisions would last after 50 men left the fort, we need to calculate the rate at which the provisions are consumed.

Step 1: Calculate the daily consumption rate:

Initially, there were 300 men and provisions for 9 days. This means that the total amount of provisions was sufficient to feed 300 men for 9 days.

Let's assume the consumption rate per man per day is C.

So, the total consumption per day for 300 men would be 300C.

Given that the provisions were enough for 9 days, we can write the equation:

300C * 9 = Total provisions

Simplifying the equation, we get:

2700C = Total provisions

Step 2: Calculate the remaining provisions after 20 days:

After 20 days, 50 men left the fort. So, the number of men remaining in the fort would be 300 - 50 = 250 men.

Now, let's calculate the remaining provisions after 20 days using the consumption rate per day (C):

Remaining provisions after 20 days = Total provisions - (300C * 20)

Step 3: Calculate the remaining days:

To find out how long the remaining provisions would last at the same rate, we can divide the remaining provisions by the consumption rate per day (C).

Remaining days = (Remaining provisions after 20 days) / C

Final Answer:

The remaining provisions would last for the calculated number of days.

Summary:

To find out how long the provisions would last after 50 men left the fort, we need to calculate the consumption rate per day. Then we can calculate the remaining provisions after 20 days and divide it by the consumption rate per day to find the remaining days.