## Percentages - Finding the Original Price

Percentage questions can be of varying difficulty and a lot of them involve reasoning of some sort.

The simplest sort of question that can be asked is for example,

Find 30% of 200:

after cancelling then cross cancelling.

More complicated questions may be for example:

The price of a car is reduced by 30% in a sale. The sale price is £5600. Find the pre – sale price.

This is illustrated below.

WE DO NOT FIND 30% OF £5600 AND ADD IT TO £5600

The simplest way is to construct a ratio table. If the car has 30% of the price subtracted that means there is 70% of the price remaining. We can construct a ratio table:

% | £ |

70 | 5600 |

100 | ? |

The scale factor the the percentages is

So the scale factor for the Price is also

The original or pre – sale price is

Example: the price of a house is reduced by !0% to £135000. Find the price of the house before the reduction.

If the house has 10% of the price subtracted that means there is 90% of the price remaining.

% | £ |

90 | 135000 |

100 | ? |

The scale factor for the % isso the scale factor for the price is also

The original price is