This problem involves calculating the duration for which provisions will last based on the number of men. It demonstrates an inverse proportion relationship: as the number of men decreases, the number of days the provisions last increases.

Understanding Provisions Calculation

We are given:

• Initial number of men ($M_1$) = 100
• Number of days provisions last initially ($D_1$) = 26
• Number of men who left = 60

Calculating Remaining Men

First, determine the number of men remaining:

Remaining men ($M_2$) = Initial men - Men who left

$M_2 = 100 - 60 = 40$ men

Calculating Duration for Remaining Men

The total amount of provisions can be thought of in terms of "man-days". The relationship between the number of men and the number of days the provisions last is inversely proportional. This can be represented by the formula:

$M_1 \times D_1 = M_2 \times D_2$

Where:

• $M_1$ = Initial number of men
• $D_1$ = Initial number of days
• $M_2$ = Remaining number of men
• $D_2$ = Number of days the provisions will last for the remaining men

Substitute the known values into the formula:

$100 \times 26 = 40 \times D_2$

Calculate the total man-days:

$2600 = 40 \times D_2$

Now, solve for $D_2$:

$D_2 = \frac{2600}{40}$

$D_2 = \frac{260}{4}$

$D_2 = 65$

Therefore, the same provisions would last for 65 days for the remaining 40 men.