A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5 ?

### Concept & Target Ratio Alligation When given the target ratio of components, first convert that target ratio into a percentage or fraction, then use alligation to find the volume ratio of the two source mixtures. $$ \text{Target Percentage} = \frac{\text{Part}}{\text{Total}} \times 100 $$ ### Step-by-Step Solution 1. Find the target percentage of water in the final mixture: - Target ratio of water to milk = $3 : 5$ - Total parts = $3 + 5 = 8$ - Target $\%$ of water = $\left(\frac{3}{8}\right) \times 100 = 37.5\%$ 2. Identify the percentage of water in the two cans: - Can 1 = $25\%$ water - Can 2 = $50\%$ water 3. Apply the Rule of Alligation using water percentages: - Can 1 proportion = $50\% - 37.5\% = 12.5\%$ - Can 2 proportion = $37.5\% - 25\% = 12.5\%$ - Ratio of Can 1 to Can 2 = $12.5 : 12.5 = 1 : 1$ 4. Calculate the volume needed from each can: - Total required volume = $12$ litres. - Since they are mixed in a $1 : 1$ ratio, divide the total volume equally. - Volume from Can 1 = $12 \times \left(\frac{1}{2}\right) = 6$ litres. - Volume from Can 2 = $12 \times \left(\frac{1}{2}\right) = 6$ litres. ### Exam Strategy & Shortcut Observe the percentages: $25\%$ and $50\%$. The target is exactly halfway between them ($37.5\%$). Therefore, they must be mixed in exactly equal parts. $12 / 2 = 6$ litres each. ### Common Pitfall Using the target ratio numbers ($3$ and $5$) directly in the alligation instead of converting them into an overall fraction or percentage ($\frac{3}{8}$). ### Final Answer Therefore, the correct answer is **6 litres, 6 litres**.