# 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%.

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