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
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