Calculate Cost Price using Sell Price and Loss Percent

How to calculate cost price using sell price and loss percent?

We know that Cost Price = Selling price + Loss

                    Cost Price = Selling Price + LossPercentage×costprice100

                    Cost Price - LossPercentage×costprice100 = Selling Price

                    Cost Price[1 - LossPercentage100] = Selling Price

                    Cost Price [100LossPercentage100] = Selling Price

Also, Cost Price = SellingPrice×100100LossPercentage (on Cross Multiplication);

Here, Selling Price and Loss% is known.

Solved examples will help us to find cost price when the selling price and loss% are known:

1. By selling a bicycle for $135, a shopkeeper loses 10%. How much percent would he gain or lose by selling it for $165?

Solution:            

Given selling price = $135                            

Loss % = 10%                                                     

We know, cost price = SellingPrice×100100LossPercentage 

                              = 135×10010010                                            

                              = 135×10090

                              = 1350010010

                              = 150

Therefore, cost price of the bicycle = $150

Now, if the selling price = $165, then gain = $165 - $150 = $15

Therefore, gain% = GainCostPrice × 100

                        = 15150 × 100

                        = 1500150

                        = 10%

Therefore, he would have gained 10%.





7th Grade Math Problems

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