# How to calculate the price of a product without the sales tax, if we know the price including the tax and the rate of the tax?

The question is

The price of a mobile phone is $8800 inclusive of a 10% GST (General Sales Tax). What is the original price of the mobile phone? This is how I approached it: The Sale Price SP of the phone, i.e. it's Original Price OP (sale price excluding GST) + GST on it, is$8800:

SP = OP + GST ---(1)


But we don't have the GST, we only have it's percentage. So let's calculate out GST from the percentage/rate:

   GST-in-Percentage = (GST / SP) * 100
=>                10 = (GST / 8800) * 100
=>               GST = 880


Now, putting values in (1):

   8800 = OP + 880
=>   OP = 8800 - 880
=>   OP = 7920


Note: I have seen it again and again, but I can't see anything wrong with the approach. But this is how they did it:

Price of the mobile = 8800
GST rate = 10%
Original Price=?
Price percent of the mobile = 100% + 10%;

By using Unitary method,

110% price = $8800 1% price = (8800 / 110) 100% price = (8800 / 110) * 100 =$8000

So the original price is $8000.  Where did I go wrong? • I can't understand your one before the last equation:$\;1\%\;$price =$\;\frac{8800}{100}\;?$By the way, your result is correct. The first part is wrong because to add ten percent to a quantity is not the same as to substract ten percent to the obtained quantity, meaning: if$\;y\;$is$\;x\;$plus ten percent of x, then it is not true that$\;x=y-$ten percent of y. Commented Feb 22, 2016 at 18:53 ## 7 Answers The other answers are correct but don't answer the question Where did I go wrong? Your problem is here: 10 = (GST / 8800) * 100 That says GST is 10 percent of 8800. but it's not. GST is 10 percent of the original price. You don't know that (yet) which is what makes the problem a little tricky. You can see your mistake more clearly if you imagine a more extreme situation. Suppose the phone cost$1000 including a 100% sales tax ...

Stick with the method the other answers teach.

• Hi, firstly thank you very much for explaining it. Secondly, in the book I have, it is written, "General Sales Tax is imposed by the Government on the percentage of the selling prices of things." So I took it as the Sale Price (the one the customer pays to buy the product). Are you sure it is calculated on the cost/buying/original price? Commented Feb 22, 2016 at 19:06
• @Solace You're welcome. I'm quite sure that "selling price" means the price of the item before tax is computed. I can understand how taking it the other way is literally true, but it would be weird in practice. Take comfort in the fact that your mistake wasn't in the mathematics, it was in reading the problem without knowing the correct idiom. Commented Feb 22, 2016 at 19:10
• Hey the dictionary definition, " the price at which something is offered for sale" source shows that it is the final price at which products are sold, so it must include the taxes, isn't it? Sorry I am a lil confused Commented Feb 22, 2016 at 23:55
• Actually I just added a question here Commented Feb 22, 2016 at 23:59

Suppose the price is $\;x\;$, so

$$x+\frac{10}{100}x=x\cdot(1.1)=8800\implies x=\frac{8800}{1.1}=8000$$

Here's a hint: $$x+\frac{x}{10}=8800$$

You just didn't compute the 10% of the original price...

HINT

$$SP=OP+GST=OP\times \Big(1+\underbrace{\frac{GST}{OP}}_{=10\%}\Big)$$

• Thanks. I thought GST was calculated on Sale Price. Commented Feb 22, 2016 at 19:07

SP = Selling price = $y$

OP = Original price = $x$

SP = OP + GST of OP

y = x + GST X

$y = x + 0.18 x$ (where GST is 18% = 0.18)

$y = x (1+0.18)$

$y = x (1.18)$

We need to know the price $x$

$x = y/1.18$

e.g.

$SP = 118$

$OP = ?$

$x = 118/1.18$

$x = 100$

It is very simple question,

Steps:

1) let us assume X as the actual price.

2) so the total amount is X(actual price)+18%(of the actual price)=2065

X+18%(X)=2065

that is equal to, X+0.18X=2065

ie, X(1+0.18)=2065

1.18X=2065

therefore, X=2065/1.18

hence X=1750

• Welcome to Mathematics Stack Exchange community! The quick tour will help you get the most benefit from your time here. Also, please use MathJax for your equations. Commented Jan 13, 2019 at 17:04