# VAT charged at 20%, so £19,800 represents 120% of price before VAT

#### ry12

##### New member
VAT charged at 20%, so £19,800 represents 120% of price before VAT

Q. A car costs £19,800 including value-added tax (VAT). The VAT is charged at 20%, so £19,800 represents 120% of the price before VAT. What is the price before VAT?

A. 10% is: £19,800 / 12 = £1,650
100% is: £1,650 * 10 = £16,500

The price before VAT is added is £16,500.

My question: Isn't 20% off of 19800 x 0.2 = 3960?
Why did he use 10%, where did he get 12 and 10 from?

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#### ksdhart2

##### Full Member
I agree with you that the solution is very poorly written. It's no wonder you're confused. However, the process the author followed is correct. What it should say is something like the following:

A car costs £19,800 including VAT. VAT is charged at 20% so £19,800 represents 120% of the price before VAT. What is the price before VAT?
10% of the price before VAT is: $$\displaystyle £19,800 \div 12 = £1,650$$
100% of the price before VAT is: $$\displaystyle £1,650 \times 10 = £16,500$$
But let's temporarily forget this solution exists and see if we can't figure how to solve the exercise another way. After that, the method the solution followed should be apparent.

You're absolutely correct that 20% of £19,800 is £3,960 and thus 80% of £19,800 is £15,840. But that's not what the question's asking for. You can try it yourself and see that this cannot be the correct answer. Suppose that the price before VAT is £15,840. We're told that a VAT of 20% is applied to the cost, so the total cost of the car should be (100% of £15,840) + (20% of £15,840) = (120% of £15,840) = 1.2 * £15,840 = £19,008. Oops! This doesn't check out. Clearly we went wrong somewhere. But where? And why?

The trick here lies in the exact same steps we did to check our answer. Let's pretend we didn't already know the answer. Let x stand for the cost of the car before VAT. Then the problem text tells us that (100% of x) + (20% of x) = (120% of x) = 1.2x = £19,800. How would you solve this equation for x? What answer does that produce? It should be the same as the given answer. How does the process you followed relate to first dividing by 12 and then multiplying by 10?

#### JeffM

##### Elite Member
Q. A car costs £19,800 including value-added tax (VAT). The VAT is charged at 20%, so £19,800 represents 120% of the price before VAT. What is the price before VAT?

A. 10% is: £19,800 / 12 = £1,650
100% is: £1,650 * 10 = £16,500

The price before VAT is added is £16,500.

My question: Isn't 20% off of 19800 x 0.2 = 3960?
Why did he use 10%, where did he get 12 and 10 from?

This is really confusing. 10% of what. A percent without describing what it is a percentage of is meaningless.

Let's leave that idiocy behind us. If I divide a number by 12 and then multiply the result by 10, that gives the same answer as dividing by 1.2.

So $$\displaystyle 19800\, \div\, 12\, \times\, 10\, \equiv\, 19800\, \div\, 1.2.$$

The .2 represents the 20% of the cost used to compute the value added tax. Messing around with 10% and 100% does not appear to relate to anything whereas 20% is meaningful in terms of the rate of tax.

ksdhart gave you the right scoop: cost with tax = cost before tax + tax = cost before tax + 20% of cost before tax = 1.2 X cost before tax

$$\displaystyle \mbox{implies cost before tax is (cost with tax)}\, \div\, 1.2\, =\, 19800\, \div\, 1.2$$

Very straightforward.

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