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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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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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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