On a particular day each of 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, and 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 of the types of pens at different prices per unit.
Assertion (A): It is possible that Danish sold each pen of Type A at a loss of Rs 2, each pen of Type B at a profit of Rs 4, and each pen of Type C at a loss of Rs 5 and made an overall profit of Rs 144; Ethan sold each pen of Type A at a profit of Rs 5, each pen of Type B at a loss of Re 1, and each pen of Type C at a profit of Rs 7 and made an overall profit of Rs 13; and Farhan sold each pen of Type A at a profit of Re 3, each pen of Type B at a profit of Re 4, and each pen of Type C at a loss of Rs 6 and made 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.