Mathematics · Linear Equations

On a particular day, Danish, Ethan, and Farhan sold three types of pens from their respective shops. Danish and Ethan sold an identical number of pens of Type A, while Farhan sold twice as many pens of Type A as Danish and Ethan together sold. The ratio of the numbers of pens of Type B sold by Danish, Ethan, and Farhan was 3:4:1 respectively. Ethan and Farhan sold an identical number of pens of Type C each, while Danish sold thrice as many pens of Type C as each of Ethan and Farhan sold. The three sellers sold each type of pen at different prices per unit. Assertion (A): It is possible that Danish sold each Type A pen at a loss of Rs 2, each Type B pen at a profit of Rs 4, and each Type C pen at a loss of Rs 5, making an overall profit of Rs 144; Ethan sold each Type A pen at a profit of Rs 5, each Type B pen at a loss of Re 1, and each Type C pen at a profit of Rs 7, making an overall profit of Rs 13; and Farhan sold each Type A pen at a profit of Re 3, each Type B pen at a profit of Re 4, and each Type C pen at a loss of Rs 6, making an overall profit of Rs 240. Reason (R): Framing and solving the system of equations derived from the profit descriptions leads to a unique solution for the total quantities of pens. Which of the following is correct?