The price of an article is ₹x. If it is bought for ₹5 less per article, 3 more articles can be bought for ₹300. What is the original price?
Answer and explanation
Correct answer: ₹25
This is a quadratic word problem involving a fixed total cost and a change in unit price. If the original price is x rupees, the original number of articles bought is 300/x. At the reduced price x − 5, the number is 300/(x − 5). The statement says the latter exceeds the former by 3: 300/(x − 5) − 300/x = 3. Combining the fractions gives 1500/[x(x − 5)] = 3, so x(x − 5) = 500. Therefore x² − 5x − 500 = 0, which factors as (x − 25)(x + 20) = 0. Price must be positive and greater than ₹5, so x = ₹25. Hence option B is correct; ₹20, ₹30 and ₹35 do not make the quantity difference equal to three.
Frequently asked questions
What is the correct answer to this question?
₹25
Why is this the correct answer?
This is a quadratic word problem involving a fixed total cost and a change in unit price. If the original price is x rupees, the original number of articles bought is 300/x. At the reduced price x − 5, the number is 300/(x − 5). The statement says the latter exceeds the former by 3: 300/(x − 5) − 300/x = 3. Combining the fractions gives 1500/[x(x − 5)] = 3, so x(x − 5) = 500. Therefore x² − 5x − 500 = 0, which factors as (x − 25)(x + 20) = 0. Price must be positive and greater than ₹5, so x = ₹25. Hence option B is correct; ₹20, ₹30 and ₹35 do not make the quantity difference equal to three.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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