In a fort there was sufficient food for 200 soldiers for 31 days. After 27 days 120 soldiers left the fort. For how many extra days will the rest of the food last for the remaining soldiers?
A)12 days
B)10 days
C)8 days
D)6 days

Options

A. 12 days
B. 10 days
C. 8 days
D. 6 days

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the total food available
The total food available is sufficient for 200 soldiers for 31 days. Therefore, the total amount of food can be calculated as follows:

\[ \text{Total Food} = \text{Number of Soldiers} \times \text{Number of Days} = 200 \times 31 = 6200 \text{ soldier-days} \]

**Hint:** Remember that "soldier-days" represents the amount of food needed for one soldier for one day.

### Step 2: Calculate the food consumed in the first 27 days
In the first 27 days, all 200 soldiers consumed food. The amount of food consumed can be calculated as:

\[ \text{Food Consumed in 27 Days} = \text{Number of Soldiers} \times \text{Number of Days} = 200 \times 27 = 5400 \text{ soldier-days} \]

**Hint:** Multiply the number of soldiers by the number of days to find out how much food has been consumed.

### Step 3: Calculate the remaining food after 27 days
To find the remaining food after 27 days, we subtract the food consumed from the total food:

\[ \text{Remaining Food} = \text{Total Food} - \text{Food Consumed} = 6200 - 5400 = 800 \text{ soldier-days} \]

**Hint:** Subtract the food consumed from the total food to find out how much is left.

### Step 4: Calculate the number of soldiers remaining after 120 leave
After 27 days, 120 soldiers leave the fort. Therefore, the number of soldiers remaining is:

\[ \text{Remaining Soldiers} = 200 - 120 = 80 \text{ soldiers} \]

**Hint:** Simply subtract the number of soldiers who left from the initial number of soldiers.

### Step 5: Calculate how many days the remaining food will last for the remaining soldiers
Now, we need to find out how many days the remaining food will last for the 80 soldiers:

\[ \text{Days Remaining} = \frac{\text{Remaining Food}}{\text{Remaining Soldiers}} = \frac{800}{80} = 10 \text{ days} \]

**Hint:** Divide the remaining food by the number of soldiers to find out how many days it will last.

### Conclusion
The remaining food will last for an additional 10 days for the remaining soldiers.

**Final Answer:** B) 10 days