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

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