120 men had provisions for 200 days. After 5 days, 30 men died due to an epidemic. The remaining food will last for how many days.

To find out how long the remaining food will last after 30 men died, we can calculate the new consumption rate and then determine how many days the remaining provisions will sustain the reduced number of men.

Initially, 120 men had provisions for 200 days, so the total provision supply is:

Total provisions = 120 men * 200 days = 24,000 man-days

Now, after 5 days, 30 men died, so there are 120 - 30 = 90 men remaining.

The total man-days available with the remaining men and provisions are:

Remaining man-days = 90 men * X days

We need to find X (the number of days the remaining food will last for the 90 men).

To calculate X, we can set up the following equation based on the principle of proportionality:

Initial man-days / Initial number of men = Remaining man-days / Remaining number of men

24,000 man-days / 120 men = X days / 90 men

Now, we can solve for X:

X = (24,000 man-days / 120 men) * (90 men) = 2,000 days

So, the remaining food will last for 2,000 days for the 90 men who are still alive.