Question : A shopkeeper sells an article at 20 percent profit. If he had bought it at a 10 percent less price and sold it for Rs. 48 less, then he would have earned a profit of 20 percent. What is the cost price of the article?
Option 1: Rs. 460
Option 2: Rs. 520
Option 3: Rs. 340
Option 4: Rs. 400
Correct Answer: Rs. 400
Solution :
Let's denote the cost price of the article as C and the selling price as S.
The shopkeeper sells the article at a 20% profit, so the selling price is
S = C + 0.2C = 1.2C
If he had bought it at a 10% less price, the new cost price would be
C = C − 0.1C = 0.9C
If he had sold it for Rs. 48 less, the new selling price would be (S − 48), and the profit earned is 20% profit.
So, S - 48 = 0.9C + 0.2 × 0.9C
⇒ 1.2C − 48 =1.08C
⇒ 0.12C = 48
⇒ C = $\frac{48}{0.12}$
⇒ C = 400
Hence, the correct answer is Rs. 400.
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