Question

There are 150 people in a camp. Food provision For them is 16 days. How many people left the camp if food lasts for 24 days?

Answer 1

$\green{\large\underline{\sf{Given \:Question - }}}$

There are 150 people in a camp. Food provision for them is 16 days. How many people left the camp if food lasts for 24 days?

Basic Concept Used :-

In the beginning, 150 men had food for 16 days. Few men say (x) left the fort, so remaining men still had food for 24 days but since x men left the fort so we can say that 150 - x men are left in the fort.

So, we have the provision of food be last for 24 days for the 150 - x men.

Here, we use the concept of indirect proportion because we know that less men, more days for the food.

Let's solve the problem now!!!

Let assume that 'x' number of men left the fort.

It is given that 150 men had food for 16 days and 150 - x men still had food for 24 days.

So, we have

$\begin{gathered}\boxed{\begin{array}{c|c|c} \bf number \: of \: men & \bf 150 & \bf 150 - x\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} &\\ \bf number \: of \: days & \sf 16 & \sf 24\\ \end{array}} \\ \end{gathered}$

So, using concept of Indirect variation, we have

$\rm :\longmapsto\:150 \times 16 = (150 - x) \times 24$

$\rm :\longmapsto\:150 \times 2 = (150 - x) \times 3$

$\rm :\longmapsto\: 300 = 450 - 3x$

$\rm :\longmapsto\: 300 - 450 = - 3x$

$\rm :\longmapsto\: - 150 = - 3x$

$\bf\implies \:x = 50$

So, it means 50 men left the fort.