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 Type A at a loss of Rs 2, Type B at a profit of Rs 4, and Type C at a loss of Rs 5 making an overall profit of Rs 144; Ethan sold Type A at a profit of Rs 5, Type B at a loss of Re 1, and Type C at a profit of Rs 7 making an overall profit of Rs 13; Farhan sold Type A at a profit of Rs 3, Type B at a profit of Rs 4, and Type C at a loss of Rs 6 making an overall profit of Rs 240. Reason (R): Framing and solving the three possible linear equations, we will find that we get a unique solution.