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?