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
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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