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****From Calculate Cost Price using Sell Price and Loss Percent to HOME PAGE**

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