My Math Forum Percentage problem - which is probably really simple!!

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 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 long-winded, 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: 17,204 Thanks: 1291 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. Thanks from Tubbyfej
March 23rd, 2017, 03:28 AM   #3
Senior Member

Joined: Apr 2014
From: Glasgow

Posts: 1,991
Thanks: 651

Math Focus: Physics, mathematical modelling, numerical and computational solutions
Quote:
 Originally Posted by Tubbyfej Hi, 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
This operation is not "reducing the gross total by 20%". To do that, you perform

$\displaystyle 110.35 \times 0.8 = 88.28$

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 Thanks from Benit13

 Tags percentage, problem, simple

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post shunya Elementary Math 1 January 5th, 2015 12:49 AM AKofTroy Elementary Math 2 July 15th, 2014 06:28 PM almozayaf Elementary Math 2 December 7th, 2013 05:24 PM hs1103 Algebra 2 October 26th, 2011 05:53 PM noon Algebra 3 November 27th, 2007 02:56 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top