# 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.

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