# 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 pr

ice = 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%.