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A shopkeeper bought an article at Rs1OOO and marked up its price by x%. If he then gave a discount of 2x/5% and still got a profit percentage of 2x/5%, find the amount of discount given? (a) 40 (b) 70 (c) 60 (d) 50?
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A shopkeeper bought an article at Rs1OOO and marked up its price by x%...
Let's assume the cost price of the article is C.
The shopkeeper marked up the price by x%. Therefore, the selling price of the article is C + (x/100)C = (100 + x)C/100.
Given that the shopkeeper gave a discount of (2x/5)% on the selling price, the discounted price is [(100 + x)C/100] - [(2x/5)(100 + x)C/100] = [(5000 + 100x - 2x^2)/(5000)] * (100 + x)C/100.
The shopkeeper still made a profit of (2x/5)%. Therefore, the profit earned is [((5000 + 100x - 2x^2)/(5000)) * (100 + x)C/100] - C = (2x/5)% of C.
We can equate the profit earned to (2x/5)% of C:
[((5000 + 100x - 2x^2)/(5000)) * (100 + x)C/100] - C = (2x/5)C.
Simplifying the equation, we get:
[((5000 + 100x - 2x^2)/(5000)) * (100 + x)/100] - 1 = 2x/5.
Solving this equation will give us the value of x, which represents the discount given by the shopkeeper.
By solving the equation, we find that x = 50.
Therefore, the amount of discount given by the shopkeeper is 50.
The correct answer is (d) 50.
The shopkeeper marked up the price by x%. Therefore, the selling price of the article is C + (x/100)C = (100 + x)C/100.
Given that the shopkeeper gave a discount of (2x/5)% on the selling price, the discounted price is [(100 + x)C/100] - [(2x/5)(100 + x)C/100] = [(5000 + 100x - 2x^2)/(5000)] * (100 + x)C/100.
The shopkeeper still made a profit of (2x/5)%. Therefore, the profit earned is [((5000 + 100x - 2x^2)/(5000)) * (100 + x)C/100] - C = (2x/5)% of C.
We can equate the profit earned to (2x/5)% of C:
[((5000 + 100x - 2x^2)/(5000)) * (100 + x)C/100] - C = (2x/5)C.
Simplifying the equation, we get:
[((5000 + 100x - 2x^2)/(5000)) * (100 + x)/100] - 1 = 2x/5.
Solving this equation will give us the value of x, which represents the discount given by the shopkeeper.
By solving the equation, we find that x = 50.
Therefore, the amount of discount given by the shopkeeper is 50.
The correct answer is (d) 50.
Community Answer
A shopkeeper bought an article at Rs1OOO and marked up its price by x%...
50
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A shopkeeper bought an article at Rs1OOO and marked up its price by x%. If he then gave a discount of 2x/5% and still got a profit percentage of 2x/5%, find the amount of discount given? (a) 40 (b) 70 (c) 60 (d) 50?
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A shopkeeper bought an article at Rs1OOO and marked up its price by x%. If he then gave a discount of 2x/5% and still got a profit percentage of 2x/5%, find the amount of discount given? (a) 40 (b) 70 (c) 60 (d) 50? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shopkeeper bought an article at Rs1OOO and marked up its price by x%. If he then gave a discount of 2x/5% and still got a profit percentage of 2x/5%, find the amount of discount given? (a) 40 (b) 70 (c) 60 (d) 50? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper bought an article at Rs1OOO and marked up its price by x%. If he then gave a discount of 2x/5% and still got a profit percentage of 2x/5%, find the amount of discount given? (a) 40 (b) 70 (c) 60 (d) 50?.
A shopkeeper bought an article at Rs1OOO and marked up its price by x%. If he then gave a discount of 2x/5% and still got a profit percentage of 2x/5%, find the amount of discount given? (a) 40 (b) 70 (c) 60 (d) 50? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shopkeeper bought an article at Rs1OOO and marked up its price by x%. If he then gave a discount of 2x/5% and still got a profit percentage of 2x/5%, find the amount of discount given? (a) 40 (b) 70 (c) 60 (d) 50? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper bought an article at Rs1OOO and marked up its price by x%. If he then gave a discount of 2x/5% and still got a profit percentage of 2x/5%, find the amount of discount given? (a) 40 (b) 70 (c) 60 (d) 50?.
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