You are Here: Home >< Maths

# Any other way? watch

1. 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
2. It doesn't seem too complicated!!

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

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

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

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: July 2, 2005
Today on TSR

### University open days

Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
• Heriot-Watt University
Wed, 21 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams