A total of 1200 rupees is spent on buying some items. If the price of each item decreases by 10 rupees, 4 more items can be bought for the same amount. What was the original price of each item?

60 rupees

Let the original price per item be \(x\) rupees. The original number of items is \(\frac{1200}{x}\), while after the price reduction it is \(\frac{1200}{x-10}\). Therefore, \(\frac{1200}{x-10}-\frac{1200}{x}=4\). Simplifying gives \(x(x-10)=3000\), or \(x^2-10x-3000=0\). Thus, \(x=60\) or \(x=-50\); a price cannot be negative, so the original price was 60 rupees. Exam tip: In price-quantity problems, express the number of items as total money divided by price and reject any impossible root.

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.