A stock of food is enough for 240 men for 48 days. How long will the same stock last for 160 men?

Options

A. 54 days
B. 60 days
C. 64 days
D. 72 days

Answer

To solve the problem step by step, we can use the concept of work and time, which states that the amount of work done (or resources used) is equal to the number of workers (or men) multiplied by the time they work (or days).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Let \( M_1 = 240 \) (number of men)
- Let \( D_1 = 48 \) (number of days)
- Let \( M_2 = 160 \) (number of men for whom we need to find the duration)
- Let \( D_2 \) be the unknown number of days.

2. **Set Up the Equation:**
According to the work and time relationship, we can set up the equation:
\[ M_1 \times D_1 = M_2 \times D_2 \]
Substituting the known values:
\[ 240 \times 48 = 160 \times D_2 \]

3. **Calculate \( 240 \times 48 \):**
First, calculate the left side:
\[ 240 \times 48 = 11520 \]

4. **Substitute Back into the Equation:**
Now, we have:
\[ 11520 = 160 \times D_2 \]

5. **Solve for \( D_2 \):**
To find \( D_2 \), divide both sides by 160:
\[ D_2 = \frac{11520}{160} \]

6. **Calculate \( D_2 \):**
Performing the division:
\[ D_2 = 72 \]

7. **Conclusion:**
Therefore, the stock of food will last for **72 days** for 160 men.