A shopkeeper marked up an article 50% above its cost price and allowed a discount of 16%. If shopkeeper received a profit of Rs 624, then find the profit percentage when shopkeeper sold the article at Rs 2880.
Question
A shopkeeper marked up an article 50% above its cost price and allowed a discount of 16%. If shopkeeper received a profit of Rs 624, then find the profit percentage when shopkeeper sold the article at Rs 2880.
Solution
Sure, 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 marked up the article by 50% above its cost price. So, the selling price before the discount is 1.5x rupees.
Step 3: The shopkeeper allowed a discount of 16%. So, the selling price after the discount is (1 - 0.16) times the selling price before the discount.
Step 4: We are given that the shopkeeper received a profit of Rs 624. To find the cost price, we need to subtract the profit from the selling price after the discount.
Selling price after discount = (1 - 0.16) * 1.5x = 0.84 * 1.5x = 1.26x
Cost price = Selling price after discount - Profit = 1.26x - 624
Step 5: We are also given that the shopkeeper sold the article at Rs 2880. To find the profit percentage, we need to calculate the profit first.
Profit = Selling price - Cost price = 2880 - Cost price
Step 6: Substitute the value of the cost price from Step 4 into Step 5 to find the profit.
Profit = 2880 - (1.26x - 624) = 2880 - 1.26x + 624 = 3504 - 1.26x
Step 7: Finally, to find the profit percentage, divide the profit by the cost price and multiply by 100.
Profit percentage = (Profit / Cost price) * 100 = (3504 - 1.26x) / x * 100
So, the profit percentage when the shopkeeper sold the article at Rs 2880 is (3504 - 1.26x) / x * 100.
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