A milk booth's rate card reads '3 litres of toned milk and 2 litres of full-cream milk cost Rs 230'. A second card at the same booth reads '9 litres of toned milk and 6 litres of full-cream milk cost Rs 690'. Can the price per litre of each kind be worked out from the two cards?

Let toned milk cost Rs $x$ and full-cream Rs $y$ a litre. The cards give $3x+2y=230$ and $9x+6y=690$. Here 3/9 = 2/6 = 230/690 = 1/3, so the second card is exactly the first multiplied by 3: the two lines coincide and there are infinitely many solutions. Physically, the second card carries no new information, so the booth has not told us enough. Both Rs 50 with Rs 40 and Rs 30 with Rs 70 really do satisfy both cards (150 + 80 = 230 and 90 + 140 = 230), and so do endlessly many other pairs, which is exactly why neither can be claimed as the answer. The cards do not contradict each other, so 'no prices fit' is wrong.