MAT Exam 2024 Paper

Concept:Profit $12.5\%$ equals $\frac{1}{8}$ of cost price, and loss $12.5\%$ equals $\frac{1}{8}$ of cost price. Use these fractions to form an equation.Explanation:Let the cost price be $x$ rupees.Selling price at $12.5\%$ profit:$$SP_1 = x + \frac{12.5}{100}x = x + \frac{x}{8} = \frac{9x}{8}$$If sold for ₹40 less, the new selling price is:$$SP_2 = \frac{9x}{8} - 40$$This new selling price gives a loss of $12.5\%$, so:$$SP_2 = x - \frac{x}{8} = \frac{7x}{8}$$Equate the two expressions:$$\frac{9x}{8} - 40 = \frac{7x}{8}$$$$\frac{9x}{8} - \frac{7x}{8} = 40$$$$\frac{2x}{8} = 40 \Rightarrow x = 160$$Thus, the cost price is ₹160.Answer:₹160 is not listed among the options, so the correct choice is Option D: None of these.