Question : Aditya sold Article X at a profit of 23% and Article Y at a loss of 13%. He earned a profit of INR 180 in the entire transaction. If article X costs INR 90 less than article Y, then what is the price of article Y (in INR)?
Option 1: 2,100
Option 2: 2,007
Option 3: 2,020
Option 4: 2,050
Correct Answer: 2,007
Solution :
Let the cost price of Y be $x$.
Cost price of X = $x-90$
Profit of X = 23% of $x-90 = 0.23x - 20.7$
Loss of Y = 13% of $x = 0.13x$
Net profit = $0.23x - 20.7 - 0.13x = 0.1x - 20.7$
So, $180 = 0.1x - 20.7$
⇒ $0.1x = 180 + 20.7 = 200.7$
⇒ $x = 2007$
Hence, the correct answer is 2007.
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