Question

In a certain state, the army was originally organized in battalions, each of 1500 men. After calling up a further 10000 recruits the army was rearranged so that there were 2000 men in each battalion and the state claimed that it had reduced its army by 50 battalions. What was the number of battalions originally?

Answer 1

Let initial number of battalions = $x$

Let initial total number of recruits = $y$

Each battalion has 1500 number of men.

So, as per question statement:

$1500 \times x = y ...... (1)$

Now, it is also given that there were 10000 new recruits,  

So, Total number of recruits = $y + 10000$

New number of men in each battalion = 2000

And, new number of battalions = $x - 50$

New equation becomes:

$y + 10000 = 2000 \times (x - 50)$

Putting value of $y$ from equation (1):

$\Rightarrow 1500 \times x + 10000 = 2000\times x - 100000\\\Rightarrow 500 \times x = 110000\\\Rightarrow x = 220$

$x$ is the initial number of battalions,

So, initial number of battalions = 220