It can't be right, can it?

A good friend of mine is a freelance IT worker with his own limited company.  He tells me that two months ago his client asked if he would work for an extra couple of hours one Saturday morning, he agreed to do the work for a fee of £100. 
He raised an invoice for his client in the sum of £100 plus VAT at 20% total £120; which the client duly paid.
At the end of the month he paid himself the additional £100 as a result his monthly payroll figures increased by the following amounts.

Income Tax	£40.00
Employers NI	£13.80
Employees NI	£2.00
Net Pay	£44.20
Total	£100.00

On the way home from work that Saturday lunchtime he stopped off at his local petrol station to top up with petrol spending £44.20, equal to just under 33 litres of petrol at £1.35 a litre.  The total spend can be broken down as follows.

Fuel Duty	£19.32
VAT	£7.37
Petrol	£17.52
Total	£44.20

Out of the total £120.00 that he invoiced his client the government received in various taxes £102.48 and he received petrol valued at £17.52.  That can't be right, can it?

He has made a mistake somewhere in his calculations, hasn't he?

Best Wishes
Will