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If a merchant makes a profit of 20% based on the selling price of an

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If a merchant makes a profit of 20% based on the selling price of an  [#permalink]

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New post 27 Feb 2018, 22:49
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Question Stats:

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If a merchant makes a profit of 20% based on the selling price of an article, what percent does the merchant make on the cost?

(A) 20

(B) 40

(C) 25

(D) 80

(E) None of these

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Re: If a merchant makes a profit of 20% based on the selling price of an  [#permalink]

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New post 27 Feb 2018, 23:24
Bunuel wrote:
If a merchant makes a profit of 20% based on the selling price of an article, what percent does the merchant make on the cost?

(A) 20

(B) 40

(C) 25

(D) 80

(E) None of these


The profit is 20% of the selling price when an article sold at 100 was bought for 80.
Here, the profit of 20 is 20% of 100, the selling price of the article!

Therefore, the profit on the cost will be \(\frac{20}{80}*100 = 25%\) (Option C)
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Re: If a merchant makes a profit of 20% based on the selling price of an  [#permalink]

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New post 28 Feb 2018, 10:54

Solution




    • Percentage Profit based on selling price \(= 20\) %

      o \(\frac{(SP – CP)}{SP} = \frac{20}{100}\)

      o \((1- \frac{CP}{SP}) = \frac{1}{5}\)

      o \(\frac{CP}{SP} = 1-\frac{1}{5} = \frac{4}{5}\)

      o Thus, \(\frac{SP}{CP} = \frac{5}{4}\)

    • We need to find the profit with respect to the cost price

      o Percentage profit \(= (\frac{SP}{CP} – 1) * 100 = (\frac{5}{4} – 1) * 100 = 25\)%

Correct Answer: Option C
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Re: If a merchant makes a profit of 20% based on the selling price of an  [#permalink]

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New post 28 Feb 2018, 19:03
Let Selling Price= 100

Profit (20% on SP)= 20

Cost Price= 100-20= 80

% profit on cost= \(\frac{20}{80}\)*100= 25

Answer: C.
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Re: If a merchant makes a profit of 20% based on the selling price of an  [#permalink]

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New post 01 Mar 2018, 17:34
Bunuel wrote:
If a merchant makes a profit of 20% based on the selling price of an article, what percent does the merchant make on the cost?

(A) 20

(B) 40

(C) 25

(D) 80

(E) None of these


We can let R = selling price and C = cost and create the equation:

R - C = 0.2R

0.8R = C

In terms of R, we see that the profit is 0.2R and the cost is 0.8R. Thus the profit as percent of cost is:

0.2R/0.8R = 0.2/0.8 = 2/8 = 1/4 = 25%

Alternate Solution:

Let’s assume the selling price is $100 and let c = the cost of the item. We know that selling price - cost = profit, or:

100 - c = 100 x 0.2

100 - c = 20

80 = c

Since the cost of the item is $80 and the profit made on its sale is $20, we see that the profit as a percent of cost is 20/80 = 1/4 = 25%.

Answer: C
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Re: If a merchant makes a profit of 20% based on the selling price of an &nbs [#permalink] 01 Mar 2018, 17:34
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