Question

A military camp has enough food for 30 days for 500 soldiers. After 6 days, 100 more soldiers came to the camp. For how many days will the remaining food last?

A) 8 days
B) 10 days
C) 12 days
D) 15 days

Answer 1

The remaining food will last for D)15 days after the arrival of an additional 100 soldiers to the military camp, following the consumption rules of proportions and ratios.

Step-by-step explanation:

The question involves a mathematical problem related to ratios and proportions. The military camp initially has enough food for 500 soldiers for 30 days. To find out how much food is consumed in 6 days by 500 soldiers, we calculate the daily consumption and then for 6 days.

This amount is subtracted from the total quantity to find the remaining food. When 100 more soldiers arrive, the total number of soldiers becomes 600.

The rate of consumption has now increased, and we need to calculate how long the remaining food will last for the increased number of soldiers. We use proportions to solve this part of the problem.

To calculate the initial daily consumption, we divide the total food quantity by 30 days:

1. Food for 1 day for 500 soldiers = Total food / 30 days.
2. Food consumed in 6 days by 500 soldiers = Food for 1 day × 6 days.
3. Remaining food = Total food - Food consumed in 6 days.
4. New daily consumption rate for 600 soldiers = (Remaining food ÷ 500 soldiers) × 600 soldiers.
5. Days the remaining food will last = Remaining food / New daily consumption rate.

Using this method, the answer can be found to be 15 days (Option D).