Question

A fort had provisions for $150$ men for $45$ days. After $10$ days $25$men left the fort. How long will the food last?

Answer 1

Given

$150$men had food for $45$ days

After $10$ days,

The remaining food would have lasted for $=\left(45-10\right)=35$days

So,$150$ men still had food for $35$ days

since, $25$ men left the fort.

So, the number of men left in the fort $=\left(150-25\right)=125$

Let us suppose that $125$men had food for $x$ number of days.

Using indirect proportion,

As the number of men decreases food will last for more days.

$$\begin{gathered} \Rightarrow 125:150::35:x \\ \Rightarrow \frac{125}{150}=\frac{35}{x} \\ \Rightarrow \frac{5}{6}=\frac{35}{x} \\ \Rightarrow 5\times x=35\times 6 \\ \Rightarrow x=\frac{35\times 6}{5} \\ \Rightarrow x=7\times 6 \\ \Rightarrow x=42 \end{gathered}$$

Hence, the food will last for $42$ days