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: Y10_Percentages_03.gif

Decreasing a quantity by a percentage:

To decrease a quantity by x percent. Calculate: Y10_Percentages_04.gif

Percentage profit and loss:

To find the percentage profit or loss of a transaction:

Calculate for profitY10_Percentages_05.gif

Calculate for lossY10_Percentages_06.gif



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.



(a) Find 8% of 300

(a) 300 × 8100 = 24

(b) Write 13 out of 20 as a percentage.

(b) 1320 × 1001 = 65%

(c) Increase 50 by 8%


(d) Decrease 50 by 8%


(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:



(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.