Calculate Cost Price using Sell Price and Profit Percent

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

We know that   cost price = selling price - profit

                      cost price = selling price - \(\frac{Profit  Percentage}{100}\) × cost price

                      cost price + \(\frac{Profit  Percentage}{100}\) × cost price = selling price

                      cost price [1 + \(\frac{Profit  Percentage}{100}\)] = selling price

                      cost price [\(\frac{100 + Profit  Percentage}{100}\)] = selling price

Also, cost price = \(\frac{Selling  Price × 100}{100 + Profit  Percentage}\); (on cross multiplication);

Here, selling price and loss% is known. 

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

1. A bag was sold for $324 thereby gaining 8%. Find the cost price of the bag.

Solution:            

Given selling price = $324                            

Gain% = 8%                                                       

We know, cost price =  \(\frac{Selling  Price × 100}{100 + Gain  Percentage}\)                  

Therefore, cost price =  \(\frac{324 × 100}{100 + 8}\)              

                              = \(\frac{324 × 100}{108}\) 

                              = 12 × 25

                              = $300                            

Therefore, the cost price of the bag is $300.

2. A book was sold for $575 thereby gaining 15%. Find the cost price of the book.

Solution:            

Given selling price = $575                            

Gain% = 15%                                                     

We know, cost price = \(\frac{Selling  Price × 100}{100 + Gain  Percentage}\)                 

Therefore, cost price = \(\frac{575 × 100}{100 + 15}\)                           

                             = \(\frac{575 × 100}{115}\)

                             = \(\frac{57500}{115}\)

                             = $500                            

Therefore, the cost price of the book is $500.    

7th Grade Math Problems

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