# 2.5 or 2.2 percent?

By Marcus Wilson 05/10/2010

So, Goods and Services Tax has now jumped from 12.5% to 15%, and with it comes all sorts of confusion. If you ask the question ‘how much have things increased?’ you can get a variety of answers?

So, an example.  Take an item that used to be priced at \$11.25.  OK, so we no longer have five cent coins – that confuses things further. So take an item priced at \$22.50 on 30 September.  The sale price as far as the retailer is concerned is \$20.00, the GST is 12.5% on that or \$2.50.

Now, go over to 1 October.  The sale price as far as the retailer is concerned is still \$20.00, but now he or she adds 15%  (or \$3.00) to that to get a new price of \$23.00.     That means as far as the consumer is concerned the price has gone up by 50 cents on \$22.50  (NOT 50 cents on \$20.00, which would be the retailer’s view) which comes to 0.50/22.5 times 100% = 2.22%).

So, if you see price tags that have increased from (say) \$100 to \$102.50  (equals 2.5%) you know the retailer is sitting there laughing, having pocketed an extra twenty eight cents while blaming it on the government.  (Just how one of my favourite chocolate bars on sale at the university  jumped overnight from \$2.00 to \$2.20 I’ll leave you to try to fathom out).

Finally, if you’re neither the consumer or the retailer, but the taxman, GST has gone up by 2.5 % ON 12.5 %, i.e. (2.5/12.5 times 100%) equals 20%.  That’s a pretty impressive increase in tax take for the government. (Of course, GST is only one source of government income).

Similar confusion occurs in some aspects of physics. An example comes from my early career, when I did some work on the processes of drying grain. The moisture content of grain is an important thing to know, and it’s often quoted as a percentage (percent water content by mass). But what does that percentage actually mean?  There are two systems – you either quote the mass of water in the grain compared to the mass of the DRY grain – the ‘dry basis’, or the mass of water in the grain compared to the TOTAL mass (dry grain plus water) – the ‘wet basis’.

So if you have a kilogram of dry grain that then absorbs 50 g of water, the percentage moisture content in the dry basis is 5%  (50 g / 1000 g times 100%); but the percentage in the wet basis is 4.8% (50 g / 1050 g times 100%). It’s important to know on which basis you are quoting the moisture content, otherwise you could end up with grain that’s too damp (goes mouldy) or spend more energy and money than needed in order to dry it.