How Much of a Total Price Is the Tax?

Date: 10/20/2003 at 08:01:59
From: Tracey
Subject: working out the vat content of an amount

How do you work out the VAT content of an amount? Eg: £55?

Date: 10/22/2003 at 09:17:02
From: Doctor Peterson
Subject: Re: working out the vat content of an amount

Hi, Tracey.

You're asking about the Value Added Tax, I believe; we handle taxes 
differently in America, showing the actual price in a store and 
adding the tax to that when it is bought. To find the VAT when you 
know only the final amount you paid, you need a little algebra.

You don't know the actual price of what you bought, so call it X. You 
do know the tax rate (but I don't!); I'll call it r. (For example, if 
the tax rate is 15%, then r=0.15.)

Then the amount you pay is

  X + rX = (1+r)X

If you know you paid Y, then you have to solve the equation

  Y = (1+r)X

for X, which you do by dividing by 1+r:

         Y
  X = -------
      (1 + r)

Finally, since you want not the original price, but the amount of tax 
you paid, you have to multiply this by r:

                r
  tax = rX = ------- * Y
             (1 + r)

So, for example, if the tax rate is 15%, you find the tax by 
multiplying the total price by (0.15)/(1.15) = 0.1304

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/