
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
March 23rd, 2017, 02:38 AM  #1 
Newbie Joined: Mar 2017 From: London Posts: 2 Thanks: 1  Percentage problem  which is probably really simple!!
Hi, I just need to say in advance that I know my problem is probably quite simple, but for some reason I have completely confused myself with this and now I need someone to explain the logic behind it as it's driving me insane and I can't continue on with my work until I have the answer: I'm trying to calculate the balance on an account  I work in accounts  and I am inputting the VAT value  which is 20% of the gross figure. Gross total: £110.35 VAT: 18.35 Net: 91.96 (round to 2.dp) The percentage problem: To calculate the net figure, I need to remove 20% of VAT from the gross total. Usually, I would divide by 1.2: 110.35 / 1.2 = 91.958333 which rounded up = 91.96 The confusion: As I understand it, when I divide the gross figure by whole number of 1 with decimal of 0.20 (1.2), this removes 20% from the figure of 110.35 What I don’t understand is when I try to remove 20% by multiplying 110.35 by 0.2 and then subtracting this from the gross figure, I get a completely different Net value. i.e. I Calculate 20% of 110.35 20/100 x 110.35 = 22.07 Then subtract this from 110:35 110.35  22.07 = 88.28 Why does dividing by 1.2 give a completely different answer to simply working out the percentage of the gross number and subtracting that from it? From my understanding on both occasions I am removing 20% of the number. But the methods give completely different answers. Sorry if this is longwinded, but any help would be much appreciated. Thanks. Fi Last edited by skipjack; March 23rd, 2017 at 03:56 AM. 
March 23rd, 2017, 03:06 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,954 Thanks: 1601 
If £n is the net price and £g is the price including VAT, g = n + 20% of n = n(1 + 20%) = n × 1.2, and so n = g/1.2. Equivalently, n = g  g/6, because 1  1/6 = 5/6 = 1/1.2. 
March 23rd, 2017, 03:28 AM  #3  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,099 Thanks: 703 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
$\displaystyle 110.35 \times 0.8 = 88.28$ But I don't think that's correct in the context of your work.  Firstly, let's set VAT to 20%. Secondly, let's remember that percentages are applied to particular values. In our case, VAT is a percentage tax applied to the net value. Repeat... it is applied to the net value. Therefore, if you start with a net value of 91.96, the gross value (net + tax) can be calculated using $\displaystyle 91.96 \times 1.2 = 110.352.$ However, what if you started with the gross value and wanted the net value? You do the inverse operation to get what you started: $\displaystyle 110.352 / 1.2 = 91.96$ And this is why you divided by 1.2.  Extra info: If you want to derive the percentage of gross value that is tax, you'll get a different value from your VAT, and rightly so because that percentage would apply to the gross value, not the net value. Different value; different percentage. The percentage is obtained using percentage = $\displaystyle \left(1  \frac{91.96}{110.352}\right) \times 100 \% = 16.\dot{6}\%$ You would then specify the relationships between net and gross values as follows: $\displaystyle 91.96 / 0.8\dot{3} = 110.352$ and $\displaystyle 110.352 \times 0.8\dot{3} = 91.96$ Notice the divide and multiplication signs have swapped from your original problem? It's because this percentage is applied to the gross value, not the net value. Last edited by skipjack; March 23rd, 2017 at 03:57 AM.  
March 23rd, 2017, 07:49 AM  #4 
Newbie Joined: Mar 2017 From: London Posts: 2 Thanks: 1 
Thank you so much for this detailed explanation!!!! It really makes sense now....you've made my day Fi 

Tags 
percentage, problem, simple 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
A simple question on percentage  shunya  Elementary Math  1  January 4th, 2015 11:49 PM 
Simple percentage problem  AKofTroy  Elementary Math  2  July 15th, 2014 06:28 PM 
Simple Question about Percentage  almozayaf  Elementary Math  2  December 7th, 2013 04:24 PM 
Simple Percentage Problem?  hs1103  Algebra  2  October 26th, 2011 05:53 PM 
Simple percentage problem  noon  Algebra  3  November 27th, 2007 01:56 PM 