A garrison of 200 men had provisions for 45 days.

Clearly, the remaining food is sufficient for 200 men for (45 − 15), i.e., 30 days.

Total number of men = 200 + 40 = 240

Let the remaining food last for x days.

Clearly, more men will take less number of days to finish the food.

So, it is a case of inverse proportion.

Now, $200 \times 30=240 \times x$

$\Rightarrow x=\frac{200 \times 30}{240}$

$\Rightarrow x=25$

∴ The remaining food will last for 25 days.