Question

A garrison of $900$ men had provisions for $42$ days. However, reinforcement of $500$ men arrived. For how many days will the food last now?

Answer 1

$\begin{array}{ccc}\text{Number of men}& 900& 1400(=900+500)\\ \text{Days}& 42& x\end{array}$

Let the required number of days be x
More men less days - It is an inverse variation.

$\Rightarrow 900\times 42=1400\times x$ [In inverse variation, product of Number of men and days will be constant]

$\Rightarrow 1400x=900\times 42$

$\Rightarrow x=\frac{37800}{1400}$

$\Rightarrow x=27$
So, the food will last for $27$ days, when reinforcement of $500$ men arrived.