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 + loss% × cost price/100

                    cost price - loss% × cost price/100 = selling price

                    cost price(1 - loss%)/100 = selling price

                    cost price(100 - loss%)/100 = selling price

Also, cost price = selling price × 100/100 - loss%  (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 = selling price × 100/100 - loss%

                            = 135 × 100/100 - 10                                                  

                            = 135 × 100/90

                            = 13500/90    

                            = 150

Therefore, cost price of the bicycle = $150

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

Therefore, gain% = gain/cost price × 100

                        = 15/150 × 100

                        = 1500/150

                        = 10%

Therefore, he would have gained 10%.





7th Grade Math Problems

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