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 ?

Answer: Option A

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)
$$\begin{array}{rl}& \therefore 800:500::24:x\\ & \iff \left(800\times x\right)=\left(500\times 24\right)\\ & \iff x=\frac{\left(500\times 24\right)}{800}\\ & \iff x=15\end{array}$$