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put this solution on YOUR website!It's a good problem, gave me pause to think and break out the pencil in paper for a second. It's easier solved if you create fake values (say that originally there's 100 products sold at 100 Euro each then make the changes and see what the product increase must be, then express it as a percentage), but I'll go through it the (slightly) harder way.
First, let's define our variables. Let's say that before the change in price & cost, the merchant was selling "x" amount of product at "y" euros/product. His pre-change income would be x times y euros.
After the change, we are told that his income rose 4%. This means that his
new income is now 1.04(xy) (100% + 4%=1.04). We know that he's now selling it at a
new rate of .8y (100%-20%=.8). To find the number of product he's now selling, we simply divide the new income by the new rate or:
In other words, he's sell 1.3 times his original sales, or selling selling 30% more product.
Looking at it in a table might make it a bit more clear:
Old sales: x products times y rate = xy income
New sales: ? products times .8y rate = 1.04xy income
And solving for our question mark we get 1.3x.
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