## Percentages

A percentage is a way of writing a fraction with a denominator of 100.

x percent, written x%, means x100 (or x parts out of 100)

### Percentage Calculations

Below are some of the types of problem that use percentages.

Percentage of a quantity:

To find x percent of a quantity. Calculate: x100 × (the quantity)

One quantity as a percentage of another quantity:

To find a out of b as a percentage. Calculate: ab × 100⁄1

Increasing a quantity by a percentage:

To increase a quantity by x percent. Calculate: Decreasing a quantity by a percentage:

To decrease a quantity by x percent. Calculate: Percentage profit and loss:

To find the percentage profit or loss of a transaction:

Calculate for profit Calculate for loss  Discount:

discount is the amount by which the price of an article is reduced.

Discount is often expressed as a percentage.

To find the cost of goods reduced by x%:

Calculate: Amount of discount = Original cost × x100

New discounted cost = original cost − amount of discount

Other types of problems involving percentages include problems with interest, depreciation, inflation and commission.

 Examples Answers (a) Find 8% of 300 (a) 300 × 8⁄100 = 24 (b) Write 13 out of 20 as a percentage. (b) 13⁄20 × 100⁄1 = 65% (c) Increase 50 by 8% (c) (d) Decrease 50 by 8% (d) (e) Calculate the % profit if a person buys a car for \$5,000 and sells it for \$6,000. (e) Profit is \$6,000 − \$5,000 = \$1,000 (f) A coat is discounted at 15% . Its original cost is \$90. What is its new cost? (f) Discount = 90 × 15⁄100 = \$13.50 New cost = \$90 − \$13.50 = \$76.50

### Finding Original Amounts

If a quantity P is increased by x% to give quantity Q then to find the original amount P: If a quantity R is decreased by x% to give quantity S then to find the original amount R: ### GST Calculations

(Goods and Services Tax, GST, is a tax used in some countries-added to the price of goods or services bought.

In some countries it is called Value-Added Tax, VAT.)

If an amount \$A excludes GST at 12.5% then to find the same amount \$B including GST: If an amount \$C includes GST at 12.5% to find the same amount \$D excluding GST: Examples Answers (a) An amount of money is increased by12% to give \$500. How much was the amount originally? (a) Let the original amount be x. The original amount was \$446.43 (b) An order for a truckload of sand was decreased by 20% to 960 kg. How much sand was originally ordered? (b) Let the original amount of sand be A kg The original amount of sand ordered was 1200 kg (c) A DVD player costs \$895 excluding GST at 12.5%. What would it cost including GST? (c) Let the cost with GST be \$y The DVD player would cost \$1006.88 including GST (d) A pie costs \$1,90 including GST. What would it cost without GST? (d) Let the cost without GST be\$p The pie would cost \$1.69 without GST.