# Percentage Discount Problem

• Dec 3rd 2008, 09:48 AM
taikahn
Percentage Discount Problem
So,

I take 10% off a line of products (in my online store) via a php script. The prices of the parts were not the same to start with.

Now I need to add the 10% back across the line of products. If I do that it obviously fails.

$100 - 10% = 90$
$90 + 10% = 99$

99$is not equal to the original$100 price.

So yeah, is there anything I can do to get back to normal pricing?

Thanks for help.
Tai
• Dec 3rd 2008, 07:10 PM
Rapha
Hi

Quote:

Originally Posted by taikahn
So,

I take 10% off a line of products (in my online store) via a php script. The prices of the parts were not the same to start with.

Now I need to add the 10% back across the line of products. If I do that it obviously fails.

$100 - 10% = 90$
$90 + 10% = 99$

99$is not equal to the original$100 price.

So yeah, is there anything I can do to get back to normal pricing?

Of course there is

x - 0.1*x = cheaper products

(e.g. 100 - 0.1*100 = 90)

-------

now you know, your product costs \$90 = cheaper product

x - 0.1*x = cheaper products

<=>
x (1-0.1) = cheaper products

x (0.9) = cheaper products

x = cheaper products / 0.9

(e .g. cheaper product = 90

->x = 90/0.9 = 100)

I hope this helps,
Rapha
• Dec 21st 2008, 01:24 AM
rick_rine@yahoo.com
• Dec 21st 2008, 02:56 AM
mr fantastic
Quote:

Originally Posted by rick_rine@yahoo.com

This is certainly a practical if all the OP wants to do is get the price back without worrying about why this works.

Let the original price be x.

Discount price: x - (10% of x) = x - 0.1 x = 0.9 x.

You want to add a percentage of the discount price to get the original price back. Consider:

0.9 x + (a % of (0.9)x) = x

$\Rightarrow 0.9 x + \frac{a}{100} \cdot (0.9 x) = x$

$\Rightarrow 0.9 + \frac{0.9 a}{100} = 1$

$\Rightarrow \frac{0.9 a}{100} = 0.1$

$\Rightarrow a = \frac{10}{0.9} = \frac{100}{9} = 11 \frac{1}{9}$

So add $11 \frac{1}{9}$%
• Dec 21st 2008, 04:25 AM
rick_rine@yahoo.com
Ours is not to reason why
Thanks mate. Your right that it is very important to understand why we do what we do in maths. It is logical and not simply a set of rules.
Thanks
Rick
• Dec 22nd 2008, 12:37 AM
The Castle
If 90 + x% of 90 = 100
x/100 * 90 =10
so, x = 100/9
So, we get 90+ 11.111111% of 90 = 100

We must remember that x% of y = y% of x i.e 9% of 10 = 10% of 9 and;10% of 9 != 9 % of 10