Mathematics · Linear Equations

On a particular day, Danish, Ethan, and Farhan sold three types of pens from their shops. Danish and Ethan sold an identical number of Type A pens, while Farhan sold 1.5 times as many Type A pens as Danish and Ethan combined. The ratio of Type B pens sold by Danish, Ethan, and Farhan was 4:3:1 respectively. Danish and Farhan sold an identical number of Type C pens each, while Ethan sold 2.5 times as many Type C pens as either Danish or Farhan. Assertion (A): It is possible that Danish sold Type A at Rs 1 loss, Type B at Rs 5 profit, Type C at Rs 3 loss, making an overall profit of Rs 114; Ethan sold Type A at Rs 4 profit, Type B at Rs 3 loss, Type C at Rs 5 profit, making an overall profit of Rs 267; and Farhan sold Type A at Rs 8 profit, Type B at Rs 5 profit, Type C at Rs 7 loss, making an overall profit of Rs 60. Reason (R): Framing and solving the three possible linear equations, we will find that we get a unique solution.