Question

A dealer sells an article for Rs.75 and gains as much per cent as the cost price of the article. Find the cost price of the article.

Answer 1

SP=75 Rs.
Let the profit% is x%.
So the cost price is x Rs.

Profit= SP- CP
= 75-x Rs.


Profit%= ×100
x= ×100
$x^2=(75-x)\times 100$
$x^2=7500-100x$
$x^2+100x-7500=0$
$x^2+150x-50x-7500=0$
$x(x+150)-50(x+150)=0$
$(x-50)(x+150)=0$

Either
x-50=0
$\to$ x=50

Or
x+150=0
x=-150 coz the value of x cannot be 0 we'll discard this value.

Hence the cost price is Rs 50
And profit% is 50%