   SEARCH HOME Math Central Quandaries & Queries  Question from bruce, a parent: Hi, i seem confused on this topic: If i need to add say 10% GST to a cost then i would times it by 1.1. If i need to reduce the cost by 10% then i need to divide it by 1.1. that is all well and good. What if i need to add 12%, 18% or 20% what is the formula then? Could someone please explain the steps / basics behind the formula. Much appreciate the assistance. Hi Bruce,

Suppose B is the cost before the tax, A is the cost after the tax is added and r is the tax rate. In your first example r = 10% = 10/100 = 0.1 and thus the tax is 0.1 × B and hence

A = B + 0.1 × B = (1 + 0.1) B

or

A = 1.1 B

which you stated. If you divide both sides of this equation by 1.1 you get

B = A/1.1

which is your second statement.

To retrace these steps for a general tax rate r the tax is r × B and hence

A = B + r × B

or

A = (1 + r) B

and thus

B = A/(1 + r).

Hence if r = 12% = 0.12 then

A = (1 + 0.12) B = 1.12 B

and

B = A/1.12

I hope this helps,
Penny

Bruce wrote back

Hi Penny, you replied to my question with this formula(i have changed the numbers):

Suppose B is the cost before the tax ($15), A is the cost after the tax is added and R is the tax rate (25%). In your first example R = 25% = 25/100 = 0.25 and thus the tax is 0.25× B=3.75 and hence A = B + 0.25 × B =$228.75 ???? but then you say: (1 + 0.25)x B....where are you getting the "1" from based on the above?? so this should be:

A=(1+0.25)*15=$18.75 correct???. but how do you get the "1"if based on your comments R=0.25*$15=3.75?? then the formula should be:

A=(3.75+0.25)*15 = $60.....that i don't think is correct. Can you please clarify. Thanks Bruce. Bruce, I took out the common factor B. B + 0.25 × B = 1 × B + 0.25 × B = (1 + 0.25) × B = 1.25 × B so when B =$15 this is

1.25 × B = 1.25 × $15 =$18.75

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.