200 persons had food provision for 48 days . If 40 persons left the place then the food will lasts for ______

Options

A. 60 days
B. 120 days
C. 40 days
D. 80 days

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the initial situation
We have 200 persons who have food provision for 48 days. This means that the total amount of food can sustain 200 persons for 48 days.

### Step 2: Calculate the total food in person-days
Total food in person-days = Number of persons × Number of days
= 200 persons × 48 days
= 9600 person-days

### Step 3: Determine the new number of persons
If 40 persons leave, the new number of persons is:
200 persons - 40 persons = 160 persons

### Step 4: Calculate how long the food will last for the new number of persons
Now we need to find out how many days the food will last for 160 persons. We have already calculated the total food in person-days, which is 9600 person-days.

Let the number of days the food will last for 160 persons be \( x \).

### Step 5: Set up the equation
The total food in person-days must equal the food consumed by the new group of persons:
\[ 160 \text{ persons} \times x \text{ days} = 9600 \text{ person-days} \]

### Step 6: Solve for \( x \)
To find \( x \), we rearrange the equation:
\[ x = \frac{9600 \text{ person-days}}{160 \text{ persons}} \]
\[ x = 60 \text{ days} \]

### Conclusion
The food will last for **60 days** after 40 persons leave.

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