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?

Question

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

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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?

Answer 1

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.

Answer 2

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

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

Answer 3

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

Answer 4

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

Answer 5

HINT

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