A man sold an article for Rs 6800 and incurred a loss. Had he sold the article for Rs7850, his gain would have been equal to half of the amount of loss that he incurred. At what price should he sell the article to have 20% profit?Options8,2507,5004,7509,000
Question
A man sold an article for Rs 6800 and incurred a loss. Had he sold the article for Rs7850, his gain would have been equal to half of the amount of loss that he incurred. At what price should he sell the article to have 20% profit?Options8,2507,5004,7509,000
Solution
Let's solve this step by step:
Step 1: Let's assume the cost price of the article is 'x'. According to the problem, the man sold the article for Rs 6800 and incurred a loss. So, we can write this as: x - 6800 = loss.
Step 2: The problem also states that if he sold the article for Rs 7850, his gain would have been half the amount of the loss. So, we can write this as: 7850 - x = 1/2 * loss.
Step 3: Now we have two equations, and we can solve them simultaneously to find the value of 'x'.
Step 4: If we substitute the value of loss from the first equation into the second equation, we get: 7850 - x = 1/2 * (x - 6800). Solving this equation gives us x = Rs 7500.
Step 5: Now, to find the selling price for a 20% profit, we calculate 20% of the cost price and add it to the cost price. So, the selling price for a 20% profit would be: 7500 + 20/100 * 7500 = Rs 9000.
So, the man should sell the article for Rs 9000 to have a 20% profit. The correct option is 9,000.
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