A garrison of 500 men had provisions for 27 days. After 3 days a reinforcement of 300 men arrived. For how many more days will the remaining food last now ?

Let the remaining food last for x days
500 men had provision for = (27 - 3) = 24 days
(500 + 300) men had provision for x days
More men, Less days (Indirect proportion)
$$\eqalign{ & \therefore \,800:500::24:x \cr & \Leftrightarrow \left( {800 \times x} \right) = \left( {500 \times 24} \right) \cr & \Leftrightarrow x = \frac{{\left( {500 \times 24} \right)}}{{800}} \cr & \Leftrightarrow x = 15 \cr} $$