The ratio of marked price to selling price of an article is 5 : 3 and shopkeeper gets a profit of 40%. If shopkeeper sells the article at its marked price, then the difference between cost price and marked price of article is Rs. 400. Find the cost price of the article?
Question
The ratio of marked price to selling price of an article is 5 : 3 and shopkeeper gets a profit of 40%. If shopkeeper sells the article at its marked price, then the difference between cost price and marked price of article is Rs. 400. Find the cost price of the article?
Solution
Let's solve the problem step by step:
Step 1: Let's assume the cost price of the article is 'x' rupees.
Step 2: The shopkeeper gets a profit of 40%, which means the selling price is 140% of the cost price. So, the selling price is (140/100) * x = 1.4x rupees.
Step 3: The ratio of the marked price to the selling price is given as 5:3. Let's assume the marked price is 'y' rupees. So, we can write the equation (y/1.4x) = (5/3).
Step 4: If the shopkeeper sells the article at its marked price, then the selling price is equal to the marked price. So, we can write the equation y = 1.4x.
Step 5: From step 3 and step 4, we have two equations: (y/1.4x) = (5/3) ----(Equation 1) y = 1.4x ----(Equation 2)
Step 6: We can solve these equations simultaneously to find the values of 'x' and 'y'.
From Equation 2, we can express 'y' in terms of 'x': y = 1.4x
Substituting this value of 'y' in Equation 1, we get: (1.4x/1.4x) = (5/3) 1 = (5/3)
Step 7: Since the equation 1 = (5/3) is not true, it means there is no unique solution for 'x' and 'y'. Therefore, the given information is inconsistent, and we cannot find the cost price of the article.
Hence, we cannot determine the cost price of the article based on the given information.
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