Discussion
In what ratio should water be mixed with a liquid costing ₹12 per litre so that by selling the mixture at ₹13.75 per litre the seller gains 25%?
Answer: B
Correct answer: 1 : 11
First convert the selling price and profit into a cost price. Selling at 13.75 with a gain of 25% means \[ \text{CP} = \frac{13.75 \times 100}{125} = 11 \text{ per litre}. \] Now apply alligation between water, which costs nothing, and the liquid at 12, with a mean of 11: \[ \frac{\text{water}}{\text{liquid}} = \frac{12 - 11}{11 - 0} = \frac{1}{11}. \] The ratio is 1 : 11. Checking: 11 litres of liquid cost 132, and the 12-litre mixture therefore costs 11 per litre; selling it at 13.75 brings in 165, a gain of 33 on 132, which is 25%. The step most often skipped is the first one - alligating on the selling price rather than converting to cost price gives the wrong ratio, because the profit has not been removed.
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