In a hostel, For 100 students food lasts for 20 days, then for how many days, the food will last if 25 more students join the hostel?

 As the number of students increases, the days for which food lasts decrease. So, this is the case of inverse proportions.  

So, x₁y₁ = x₂y₂

$\Rightarrow 100 \times 20 = (100 + 25 ) \times {\mathrm{y}}_2$

$\Rightarrow {\mathrm{y}}_2 = \frac{100 \times 20}{125}$

$\Rightarrow {\mathrm{y}}_2 = 16 \mathrm{days}$

Hence, the food will last for 16 days.