Percentage problem - which is probably really simple

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tubbyfej
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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 the subtracting this from 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
 
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tubbyfej said:
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 the subtracting this from 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

subtraction 20% is same as finding 80% of the same or multiplying by .80

deviding by 1.2 is not same as \finding 80% you get 100/1.2 = 83.3 %

hence there is discripency
 
Hi kaliprasad,

Thanks for the response! But I am still confused!

When excluding VAT i.e reducing by 20% - it is common practice to divide by 1.2 - please see UK Government website:

https://www.gov.uk/vat-businesses/inclusive-exclusive-prices

If this method actually give 83.3% of the gross figure and not the 80% as you would expect, then why is it used?

I should also mention that I am using VAT as an example but I have seen this approach of reducing a number by a percentage by dividing it using the (1.xx) approach.

I am confused as to when it appropriate to use which method.

Method A:
Calculate the percentage of the number - then subtract from the number - (this seems the most logical to me)

Method B:
Divide (or multiply) the number by 1.xx to Reduce (or add on) the percentage amount.

You've explained why there is a discrepancy but I just want to know why the two different methods are used for effectively adding or subtracting a percentage.

And how do you know when to apply which method?

Thanks