Question : A person sells an article for a loss of 18%. If he increases the selling price by INR 144 and decreases the cost price by 30%, then there is a profit of 20%. What is the original selling price?
Option 1: INR 5,068
Option 2: INR 6,036
Option 3: INR 5,904
Option 4: INR 6,124
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Correct Answer: INR 5,904
Solution : Given: A person sells an article for a loss of 18%. Let the selling price (SP) and cost price (CP) of an article be INR $x$ and INR $y$ respectively. Profit $=x–y$ Loss $=y–x$ Profit percentage $=\frac{(x–y)}{y}\times 100$ Loss percentage $=\frac{(y–x)}{y}\times 100$ According to the question, $18=\frac{(y–x)}{y}\times 100$ (equation 1) ⇒ $0.18=1–\frac{x}{y}$ ⇒ $\frac{x}{y}=1–0.18$ ⇒ $\frac{x}{y}=0.82$ ⇒ $x=0.82y$ Also, $20=\frac{(x+144)–(y–0.3y)}{y–0.3y}\times 100$ (equation 2) Substitute the value from equation (1) to equation (2), we get, $0.2\times0.7y=0.82y+144–0.7y$ ⇒ $0.02y=144$ ⇒ $y=$ INR 7200 So, $x=0.82\times7200=$INR 5,904. Hence, the correct answer is INR 5,904.
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