help please

I don't think that is quite right Takahiro,

Say something costs $100 and you have to add 10%gst that makes it cost $110.

If you want to go backwards you cannot say 10% of $110=$11 so the pre GST price was 110-11=$99.

You see, it is 10% of the pre taxed price not 10% of the hight price!

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I am going to let the original price be $x

It was reduced by 20% so the new price will be 80% of the original price.  That is 0.8x

Now 10% GST is added that means the price will  be 110% of 0.8x = 1.1*0.8x = 0.88x

Nlow 0.88x=$120

x=120/0.88

x=$136.36 to the nearest cent.  

Let's solve this!

Firstly we need to take off the GST. The Tax is 10% of the price and will change according to the price. So, 120 lets take off 10%. That will be 120-12. The answer to that is 108. Now that we have this, we know that the Original price multiply by 0.8 will be 108. What this means is that this price is 80% of the full original. So lets do this:

$${\frac{{\mathtt{108}}}{{\mathtt{80}}}} = {\frac{{\mathtt{27}}}{{\mathtt{20}}}} = {\mathtt{1.35}}$$

Now lets multiply this by 100.

$${\mathtt{1.35}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\mathtt{135}}$$

Lets not stop here. We will need the GST. Which is 10%

What is 10% of 135?

$${\mathtt{135}}{\mathtt{\,\small\textbf+\,}}{\mathtt{13.5}} = {\frac{{\mathtt{297}}}{{\mathtt{2}}}} = {\mathtt{148.5}}$$

The Original Price was 148.5