Mathematics · Linear Equations

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