Generate a formula for x in my case

Question

Kindly see the following,

Gross Total              :      10000
Discount                 :          0
Tax % : 10    Tax Amount :       1000
                         ------------
Net Total                :      11000

Formula: 

Tax Amount = (Gross Total - Discount) * Tax % / 100
Net Total  = (Gross Total - Discount + Tax Amount)

Now what i try to accomplish here is, Whenever changing the Net total, the discount amount should be calculated accordingly. By the way tax % is read only. Then Based on the new discount the tax amount should be calculated and hence the (Gross total - discount + tax amount) should match the new given net total.

So in order to achieve it, I just framed an equation like below,

Gross total - x + [(Gross total - x) * tax % / 100] = Net total

where x is the discount amount to be calculated.

Can anybody tell me whether the above equation framed by me is right or wrong.? If right then can you show how to define a formula to find the x.? else Kindly guide me to achieve my requirement in a clean way. I meant accurate way.

Answer 1

Your formula is correct. As for finding a formula for $x$ in terms of the other amounts, let $G$ be the gross total, $T$ be the tax rate, $N$ be the net total. Then, with $x$ the discount as you have it, you want $$G-x+(G-x)\cdot\frac{T}{100}=N$$ $$(G-x)\cdot\left(1+\frac{T}{100}\right)=N$$ $$(G-x)\cdot\frac{100+T}{100}=N.$$ Can you solve that last equation for $x$ in terms of the other variables?