A shopkeeper allows a discount of 30% on marked price of an article and customer also managed to get additional 10% discount on discounted price and in this way get a total discount of Rs.925. If shopkeeper incurs a loss of on selling the article then find its cost price for the shopkeeper?
Question
A shopkeeper allows a discount of 30% on marked price of an article and customer also managed to get additional 10% discount on discounted price and in this way get a total discount of Rs.925. If shopkeeper incurs a loss of on selling the article then find its cost price for the shopkeeper?
Solution
Let's solve the problem step by step:
Step 1: Let's assume the cost price of the article for the shopkeeper is 'x' rupees.
Step 2: The shopkeeper allows a discount of 30% on the marked price. So, the selling price after the first discount will be (100% - 30%) of the marked price, which is 70% of the marked price.
Step 3: The customer manages to get an additional 10% discount on the discounted price. So, the selling price after the second discount will be (100% - 10%) of the discounted price, which is 90% of the discounted price.
Step 4: The total discount obtained by the customer is Rs. 925. We can set up the equation as follows:
0.9 * 0.7 * x = x - 925
Step 5: Simplifying the equation, we get:
0.63x = x - 925
Step 6: Bringing all the 'x' terms to one side and the constant terms to the other side, we get:
0.37x = 925
Step 7: Dividing both sides of the equation by 0.37, we get:
x = 925 / 0.37
Step 8: Evaluating the right side of the equation, we find:
x = 2500
Therefore, the cost price of the article for the shopkeeper is Rs. 2500.
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