Janki sold her leather purse at 8 percent loss. If she had sold it for 150 rupees more, she would have made a profit of 12 percent. Find selling price of thepurse
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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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How to calculate selling price using cost and loss percent?
We know, Selling Price = cost price - loss
Selling Price = cost price - \(\frac{Loss Percentage × Cost Price}{100}\)
Selling Price = \(\frac{100 × Cost Price - Loss Percentage × Cost Price}{100}\)
Selling Price = Cost Price (\(\frac{100 - Loss Percentage}{100}\)), [Here, cost price and loss% are known.]
Solved examples will help us to find selling price when the cost price and loss% are known:
1. Shelly bought a dress for $150 and sold it to Jenny there by suffering a loss of 10%. Find the selling price of the dress.
Solution:
Given cost price = $150
Loss % = 10%
We know, selling price = Cost Price (\(\frac{100 - Loss Percentage}{100}\))
= 150 (\(\frac{100 - 10}{100}\))
= 150 (\(\frac{90}{100}\))
= (\(\frac{150 × 90}{100}\))
= 9 × 15
= $135
Therefore, selling price of the dress is $135.
2. Mike bought a laptop for $800 and sold it to Jack there by suffering a loss of 12%. Find the selling price of the laptop.
Solution:
Given cost price = $800
Loss % = 12%
We know, selling price = Cost Price (\(\frac{100 - Loss Percentage}{100}\))
= 800 (\(\frac{100 - 12}{100}\))
= \(\frac{800 × 88}{100}\)
= 88 × 8
= $724
Therefore, selling price of the laptop is $724.
3. By selling a chair for $372, Daisy loses 7%. At what price must she sell it to gain 10%.
Solution:
Given selling price = $ 372
Loss % = 7%
We know, Cost Price = \(\frac{Selling Price × 100}{100 - Loss Percentage}\)
Therefore, cost price = \(\frac{372 × 100}{100 - 7}\)
= \(\frac{372 × 100}{93}\)
= $400
Now cost price = $400
Gain% = 10%
Therefore, selling price = Cost Price [\(\frac{100 + Gain Percentage}{100}\)]
= 400 [\(\frac{100 + 10}{100}\)]
= 110 × 4
= $440
7th Grade Math Problems
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