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    • Thread Starter

    In country X the V.A.T. went up by 20% however, this was only an increase of 4% in the prices. What was the original V.A.T and what is it now?

    I am a little ashamed as it took me longer than I expected to work this question out. I believe this is not even GCSE level. I worked it out using simultaneous equations. They got pretty complicated and that's why it took me so long. However, I couldn't see any other way. There must be though...I just can't see it. Happens all the time

    It doesn't seem too complicated!! :cool:

    P = original product price
    P1 = original product cost = (1+V1)*P where V1 = original VAT

    P2 = new product cost = (1+V2)*P where V2 = new VAT

    V2= 1.2*V1 - 20% increase in VAT
    P2 =1.04*P1 - 4% increase in purchase price
    (1+V2)*P = 1.04*(1+V1)*P

    now substitute for V2 = 1.2*V1

    1 + 1.2Y1 = 1.04 + 1.04V1
    0.16V1 = 0.04
    V1 = 4/16
    V1 = 1/4
    V1 = 0.25
    • Thread Starter

    Yes. I did it by writing them in the form of ratios then forming simultaneous equations from them.
    x=original VAT
    y=new VAT

    x : y
    =>100y - 120x=0

    100 : 104
    1 + x : 1 + y
    104 + 104x = 100 + 100y
    104x - 100y = -4...(1)
    120x - 100y = 0...(2)
    (2) - (1)
    16x = 4
    x = .25 or 25%
    y = 25% * 1.2
    y = .3 or 30%
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Updated: July 2, 2005

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