MAT Exam 2024 Paper

Concept:Set up equations from the two selling conditions using cost prices of the laptop and printer.Explanation:Let the cost price of the laptop be $x$ and the cost price of the colour printer be $y$.In the first case, there is no overall loss or gain.Loss on laptop $= 12.5\%$ of $x = \frac{1}{8}x$Gain on printer $= 25\%$ of $y = \frac{1}{4}y$So, $\frac{1}{8}x = \frac{1}{4}y$This gives $x = 2y$.In the second case, there is a total loss of ₹1200.Gain on laptop $= 8\%$ of $x = 0.08x$Loss on printer $= 20\%$ of $y = 0.20y$Net loss is $0.20y - 0.08x = 1200$.Substitute $x = 2y$ into the equation:$0.20y - 0.08(2y) = 1200$$0.20y - 0.16y = 1200$$0.04y = 1200$$y = ₹30000$Answer:He paid $₹30{,}000$ for the colour printer.