# PS: Percentage Reduction Lesson Progress
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####  Problem-solving is a very necessary skill that you need to develop in math and it is about applying your knowledge and understanding to general questions.

Let us take a look at some of these questions.

### Example 1

In a sale, an item is reduced by 20% and as a result, the shop keeper only makes 4% profit on the item.

What percentage profit would the shopkeeper have made it the item was sold at full price?

Since we don’t know what the cost price is, we label it as ‘C’. And we do the same thing for the selling price, by labelling it as ‘S’

What the question actually tells us though, is the relationship between ‘C’ and ‘S’.

And we can put this relationship in an algebra format by saying 0.8 ‘s’ = 1.04 ‘c’

We get the 0.8 by taking 20% off of 100% to be left with 80%

And we get the 1.04 by adding 4% to 100%

This means that we can re-arrange our equation in such a way that we can say the selling price ‘s’ is equal to 1.04 divided by 0.8 times ‘c’ which can be simplified to 1.3 × ‘c’

This means that the selling price would have produced a 30% profit (1.3 = 130%) if it were not reduced in the sale.