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 + \(\frac{Loss Percentage × cost price}{100}\)

                    Cost Price - \(\frac{Loss Percentage × cost price}{100}\) = Selling Price

                    Cost Price[1 - \(\frac{Loss Percentage}{100}\)] = Selling Price

                    Cost Price [\(\frac{100 - Loss Percentage}{100}\)] = Selling Price

Also, Cost Price = \(\frac{Selling Price × 100}{100 - Loss Percentage}\) (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 = \(\frac{Selling Price × 100}{100 - Loss Percentage}\) 

                              = \(\frac{135 × 100}{100 - 10}\)                                            

                              = \(\frac{135 × 100}{90}\)

                              = \(\frac{13500}{100 - 10}\)

                              = 150

Therefore, cost price of the bicycle = $150

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

Therefore, gain% = \(\frac{Gain}{Cost Price}\) × 100

                        = \(\frac{15}{150}\) × 100

                        = \(\frac{1500}{150}\)

                        = 10%

Therefore, he would have gained 10%.

7th Grade Math Problems

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