Let:

• x be the initial petrol consumption.
• y be the number of days the petrol lasts initially.

According to the question:

• Initially, the petrol lasts for 10 days with a consumption of x.
• After the consumption increases by 25% each day, the final consumption on the last day will be $(\frac{125}{100}) \cdot x$.

This is a case of indirect variation, meaning that the product of the consumption and the number of days remains constant.

So, we have the relation:

$x \cdot 10 = (\frac{125}{100}) \cdot x \cdot y$

Now, solving for y (the number of days the petrol will last after the increase in consumption):

$10x = (\frac{125}{100}) \cdot x \cdot y$

Dividing both sides by $(\frac{125}{100}) \cdot x$:

$y = 10 / (\frac{125}{100}) = 10 / 1.25 = 8$

Thus, the petrol will last for:

8 days.