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
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