In a fort, provisions are sufficient for 1600 soldiers for 30 days, if each soldier cnsumes at the rate of 2.5 kg per day. If 400 more soldiers join the fort and now each soldier consumes 3 kg per day, for how many days will the provisions last?

Options

A. 15
B. 10
C. 20
D. 12

Explanation

To solve the problem step by step, we need to first calculate the total provisions available and then determine how long those provisions will last with the new number of soldiers and their consumption rate.

### Step 1: Calculate the total provisions available

The total provisions can be calculated based on the number of soldiers, the number of days, and the consumption per soldier.

- Number of soldiers = 1600
- Number of days = 30
- Consumption per soldier per day = 2.5 kg

Total provisions = Number of soldiers × Number of days × Consumption per soldier per day

\[ \text{Total provisions} = 1600 \, \text{soldiers} \times 30 \, \text{days} \times 2.5 \, \text{kg/soldier/day} \]

\[ \text{Total provisions} = 1600 \times 30 \times 2.5 = 120000 \, \text{kg} \]

### Step 2: Determine the new number of soldiers

After 400 more soldiers join, the new total number of soldiers is:

\[ \text{New number of soldiers} = 1600 + 400 = 2000 \, \text{soldiers} \]

### Step 3: Determine the new consumption rate

The new consumption rate per soldier is given as 3 kg per day.

### Step 4: Calculate the total daily consumption of the new soldiers

Now, we need to calculate the total daily consumption for the new number of soldiers:

\[ \text{Total daily consumption} = \text{New number of soldiers} \times \text{New consumption rate} \]

\[ \text{Total daily consumption} = 2000 \, \text{soldiers} \times 3 \, \text{kg/soldier/day} = 6000 \, \text{kg/day} \]

### Step 5: Calculate how many days the provisions will last

Now, we can find out how many days the provisions will last with the new daily consumption:

\[ \text{Number of days provisions will last} = \frac{\text{Total provisions}}{\text{Total daily consumption}} \]

\[ \text{Number of days provisions will last} = \frac{120000 \, \text{kg}}{6000 \, \text{kg/day}} = 20 \, \text{days} \]

### Final Answer

The provisions will last for **20 days**.

---