A garrison of 200 men had provisions for 45 days.
Question:

A garrison of 200 men had provisions for 45 days. After 15 days, 40 more men join the garrison. Find the number of days for which the remaining food will last.

Solution:

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.