Discussion
In what ratio must water be mixed with milk costing ₹32 per litre to obtain a mixture worth ₹28 per litre?
Answer: C
Correct answer: 1 : 7
Water is free, so treat its price as zero and apply alligation between 0 and 32 with a mean of 28: \[ \frac{\text{water}}{\text{milk}} = \frac{32 - 28}{28 - 0} = \frac{4}{28} = \frac{1}{7}. \] The ratio is 1 : 7 - one litre of water to seven of milk. Checking: 7 litres of milk cost \( 7 \times 32 = 224 \), and the mixture is 8 litres, so the rate is \( 224/8 = 28 \) per litre as required. The whole of the trick with this family of questions is recognising that water costs nothing, which turns a dilution problem into an ordinary alligation. A related form asks for the profit from such adulteration: selling the 8-litre mixture at the milk price of 32 brings in 256 against a cost of 224, a gain of 32 on 224, which is \( 14\frac{2}{7}\% \).
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