A shopkeeper bought x items for 720 rupees. If he had received 3 more items for the same total amount, the cost per item would have been 40 rupees less. What is the value of x?
Answer and explanation
Correct answer: 6
The original cost per item is \(\frac{720}{x}\), and with 3 additional items it would be \(\frac{720}{x+3}\). Therefore, \(\frac{720}{x}-\frac{720}{x+3}=40\). On simplification, \(x^2+3x-54=0\), or \((x-6)(x+9)=0\). Thus \(x=6\) or \(x=-9\); since the number of items cannot be negative, \(x=6\) is the valid answer. Exam tip: In word problems involving quantities, reject any negative root.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The original cost per item is \(\frac{720}{x}\), and with 3 additional items it would be \(\frac{720}{x+3}\). Therefore, \(\frac{720}{x}-\frac{720}{x+3}=40\). On simplification, \(x^2+3x-54=0\), or \((x-6)(x+9)=0\). Thus \(x=6\) or \(x=-9\); since the number of items cannot be negative, \(x=6\) is the valid answer. Exam tip: In word problems involving quantities, reject any negative root.
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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