5 - Percentage increase and decrease
During your GCSE Maths exam, you may also be asked to find the percentage increase or decrease of the price of a certain item. In order to calculate these values, you must find one amount as a percentage of another. To do this, you must form a fraction from the two amounts and multiply this by 100.
(a) - £500 is borrowed for 6 years at an interest rate of 5% per annum (i.e. each year). Calculate the interest generated.
(a) - This type of question is referred to as a simple interest problem, because the amount of money borrowed remains fixed.
First you must calculate the amount of interest generated after one year, which is 5% of £400
5% of £500= 5/100× 500/1= 2500/100= 25
Therefore the amount of interest generated after one year is £25
The question is asking you to generate the amount of interest after 6 years, so you must multiply this value by 6
25 x 6 = 150
Therefore the amount of interest generated after 6 years = £150
This simple interest process can be memorised using the formula:
Interest = P × R × T
- P (principal) is the amount borrowed.
- R is the rate of interest per year.
- T is the time in years.
You may also be asked to solve a profit and loss question. This type of percentage based question involves an item being bought at one price and sold for another.
If the selling price is greater than the buying price, a profit is made.
If the selling price is less than the buying price, a loss occurs.
(b) - Sarah buys a TV for £90 and sells it for £120. What is her percentage of profit made?
(b) - First you must work out the amount of profit made. The cost price is £90 and the selling price is £120, so the profit made is:
£120-£90 = £30
To calculate Sarah's percentage profit, you must calculate this profit value as a percentage of the original price of the TV. To do this, you must divide the profit by the original price and multiply the value by 100:
30 ÷120 = 0.25
0.25 x 100 = 25
Therefore the percentage profit made is £25%.
(c) - Darren buys a games console in a sale for £90. The original cost of the console was £250. What is the percentage decrease of the games console?
(c) - Darren bought the games console for £90 and the original price was £250. Therefore the loss which has occurred is:
£250 - £90 = £160
To calculate the percentage decrease, you must divide the actual decrease by the original price and multiply this value by 100:
0.64 x 100= 64
Therefore the percentage decrease which has occurred is 64%.