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

x percent, written x%, means ^{x}⁄_{100} (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: ^{x}⁄_{100} × (the quantity)

**One quantity as a percentage of another quantity:**

To find a out of b as a percentage. Calculate: ^{a}⁄_{b} × 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**:

A **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 × ^{x}⁄_{100}

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 × |

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

(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 = $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:

ExamplesAnswers(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

includingGST?(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

withoutGST?(d) Let the cost without GST be$p

The pie would cost $1.69 without GST.