A shopkeeper sells \((60-x)\) items at the rate of \(x\) rupees per item. If his total revenue is 875 rupees, what is the smaller value of \(x\)?
Answer and explanation
Correct answer: 25
Total revenue equals price per item multiplied by the number of items, so \(x(60-x)=875\). Rearranging gives \(x^2-60x+875=0\), or \((x-25)(x-35)=0\). Thus, \(x=25\) or \(x=35\), and the smaller value is 25. Exam tip: In such problems, first form the revenue equation and then select the required root from the two solutions.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
Total revenue equals price per item multiplied by the number of items, so \(x(60-x)=875\). Rearranging gives \(x^2-60x+875=0\), or \((x-25)(x-35)=0\). Thus, \(x=25\) or \(x=35\), and the smaller value is 25. Exam tip: In such problems, first form the revenue equation and then select the required root from the two solutions.
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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