Inverse Proportion in Food Stock Problems

This problem involves an inverse relationship between the number of men and the number of days a fixed stock of food will last. When the number of men decreases, the duration the food lasts increases, and vice versa.

Calculating Total Food Stock

The total amount of food can be measured in 'man-days', which represents the number of days one man can be fed. We calculate this using the initial information:

Total Food Stock = Number of Men $\times$ Number of Days

Using LaTeX for clarity:

$ \text{Total Stock} = N_1 \times D_1 $

Where:

• $ N_1 = 240 $ men
• $ D_1 = 48 $ days

$ \text{Total Stock} = 240 \text{ men} \times 48 \text{ days} = 11520 \text{ man-days} $

Duration for 160 Men

Now, we need to find out how long this same stock (11520 man-days) will last for a different number of men ($ N_2 = 160 $).

Let the new duration be $ D_2 $ days.

The relationship remains:

$ \text{Total Stock} = N_2 \times D_2 $

We can set up the equation:

$ 11520 \text{ man-days} = 160 \text{ men} \times D_2 \text{ days} $

To find $ D_2 $, we rearrange the equation:

$ D_2 = \frac{11520 \text{ man-days}}{160 \text{ men}} $

$ D_2 = 72 \text{ days} $

Conclusion

The same stock of food will last for 72 days for 160 men.