Question

A businessman bought some items for rs 7500 . he kept 5 items for himself and sold the remaining items at a profit os rs 25 per item. from the amount received he could buy 6 more items. find the original price of each item?

Answer 1

First, let the total number of items he bought originally be x

So the profit he got will be 25(x-5) since he kept 5 items for himself.

The profit he got is enough for him to to buy 6 more items which is $6(\frac{7500}{x} )$

So you can create an equation like this 
$25(x-5)=6(\frac{7500}{x} )$

$25x-125=\frac{45000}{x} )$
$25 x^{2} -125x=45000$
$25 x^{2} -125x-45000=0$
$x^{2} -5x-1800=0$

Solving this quadratic equation, you will get 45 or -40. Since x is the number of items he bought, we can reject -40. 

So the total number of items he bought is 45.

The original cost of each item will be 7500/45 = 166.67 (or $166 \frac{2}){3}$