find cost price

**neha1** · May 23rd 2008, 08:42 PM

a man sells an article at a profit of 25%.if he had bought it at 20% less and sold it for the amount 10.50 less,he would have gained 30%.find the cost price of article?

**Moo** · May 23rd 2008, 10:59 PM

Hello,

Originally Posted by hena

a man sells an article at a profit of 25%.if he had bought it at 20% less and sold it for the amount 10.50 less,he would have gained 30%.find the cost price of article?

Let X be the cost price of the article, and let Y be the price he sells the article the first time.

1st sentence
Making a profit of 25% is like selling it to 1.25 times the cost price.

So $\boxed{Y=1.25 ~X}$

2nd sentence
If he had bought it 20% less, it means that the cost price becomes $0.80 ~X$
If he sells it for the amount 10.50 less, this means that he sells it at the price $Y-10.50$

While doing this, he makes a profit of 30%. So reasoning just as before, we get :

$\boxed{(0.80 ~\cdot X) ~\cdot 1.30=Y-10.50}$

Now, solve for X

**neha1** · May 25th 2008, 08:19 AM

am not getting aproper value of x...
plz help me out..
the option they gave me is
55,45,50,60

**Moo** · May 25th 2008, 08:23 AM

Originally Posted by hena

am not getting aproper value of x...
plz help me out..
the option they gave me is
55,45,50,60

Well, I get 50...

$Y=1.25 X$

Substituting in $(0.80 ~\cdot X) ~\cdot 1.30=Y-10.50$ :

$(0.80 ~\cdot X) ~\cdot 1.30=1.25 X-10.50$

0.8*1.3=1.04

$1.04 X=1.25 X-10.50$

$0.21 X=10.50$

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find cost price

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