Question : Vinay sells an article at a profit of 20%. If both the cost price and selling price are reduced by Rs. 20, then the profit becomes 40%. What is the initial cost price?
Option 1: Rs. 80
Option 2: Rs. 60
Option 3: Rs. 50
Option 4: Rs. 40
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Correct Answer: Rs. 40
Solution : Let the initial cost price = $100x$ A profit of 20% means the selling price = $120x$ As both were reduced by Rs. 20. New cost price = $100x - 20$ New selling price = $120x - 20$ Profit = $(120x - 20 - 100x + 20)$ Now the new profit is 40%. So, $\frac{(120x - 20 - 100x + 20)}{(100x - 20)}\times 100 = 40$ ⇒ $\frac{20x}{(100x - 20)} = \frac{2}{5}$ ⇒ $100x = 200x - 40$ ⇒ $100x = 40$ Since the initial cost price is $100x$ and the value of $100x = 40$ Hence, the correct answer is Rs. 40.
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