Discussion
In what ratio should water be mixed with wine that costs Rs. 60 per litre so that after selling the resultant mixture at Rs.50 per litre, the profit will be 25%?
Answer: A
Water and wine must be mixed in the ratio 1 : 2.
Selling at Rs 50 per litre gives a 25% profit, so the cost price of the mixture is
\[ \frac{50}{1.25} = 40 \text{ rupees per litre} \]
Water costs nothing and wine costs Rs 60, so by alligation:
\[ \begin{aligned} \text{water} : \text{wine} &= (60 - 40) : (40 - 0) \\ &= 20 : 40 = 1 : 2 \end{aligned} \]
Check: 1 litre of water and 2 litres of wine cost Rs 120 for 3 litres, Rs 40 a litre. The other ratios give a cost of Rs 36 (2 : 3), about Rs 34.3 (3 : 4) and about Rs 33.3 (4 : 5), so the profit would not be 25%.
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