Mathematics · Linear Equations

On a particular day, Danny, Edwin, and Fahim sold three types of pens from their respective shops. Each of them sold an identical number of pens of Type A, an identical number of pens of Type B, and an identical number of pens of Type C. However, the numbers of pens of each type sold were all different from one another. Also, the three sellers sold each type of pen at different prices per unit. Assertion (A): It is possible that Danny sold each pen of Type A at a profit of ₹2, each pen of Type B at a loss of ₹1, and each pen of Type C at a loss of ₹12 and made an overall profit of ₹8; Edwin sold each pen of Type A at a profit of ₹2, each pen of Type B at a loss of ₹6, and each pen of Type C at a loss of ₹6 and made an overall profit of ₹14; and Fahim sold each pen of Type A at a profit of ₹1, each pen of Type B at a profit of ₹1, and each pen of Type C at a loss of ₹3 and made an overall profit of ₹27. Reason (R): Framing and solving the three possible linear equations, we will find that we get a unique solution.