Mixture and Alligation - Solved Questions and Answers Last Updated : 25 Jun, 2025 Comments Improve Suggest changes Like Article Like Report Question 1: From a vessel of 20 liters of pure milk, 1 liter is taken out and replaced with water, so as to keep the volume constant at 20 liters. This process is repeated 5 times. Find the percentage of pure milk left in the vessel after 5 replacements. Solution: Here, we need to apply the formula [1 - (R / P)] n P = Initial quantity of pure element = 20 liters R = Quantity replaced every time = 1 liter (volume removed and replaced each time) n = Number of replacements = 5 So, the quantity of pure milk after 5 replacements = [1 - (1 / 20)]5Quantity of pure milk after 5 replacements (0.95)5 = 0.7737809375 Therefore, percentage of pure milk left in the vessel after 5 replacements = (0.7737809375) x 100 = 77.378 % Question 2: A dishonest shopkeeper mixed cheaper quality rice, priced at Rs. 10 / KG with good quality rice, priced at Rs. 25 / KG, and sold the mixture at Rs. 15 / KG. Find the ratio in which he mixes the two qualities of rice. Solution: Thus, the ratio of quantities of cheaper and good quality rice = 10: 5 = 2: 1Question 3: A grocer mixes two varieties of rice costing $15 per kg and $20 per kg in the ratio 2:3. What is the price per kg of the resulting mixture?Solution:Using the alligation formula:Mean Price = \frac{(15 \times 2) + (20 \times 3)}{2 + 3} = \frac{30 + 60}{5} = \frac{90}{5} = 18Therefore, the price per kg of the mixture is $18.Question 4: A vessel contains 60 liters of milk. 12 liters of milk are taken out and replaced with water. If this process is repeated once more, how much milk is now in the vessel?Solution:First Removal: Milk left after first replacement = 60 \times \left(1 - \frac{12}{60}\right) = 60 \times \frac{48}{60} = 48 LitresSecond Removal: Milk left after second replacement = 48 \times \left(1 - \frac{12}{60}\right) = 48 \times \frac{48}{60} = 38.4 liters.Therefore, the milk remaining in the vessel is 38.4 liters.Question 5: How much water must be added to 40 liters of a 20% alcohol solution to make it a 10% alcohol solution?Solution:20% of 40 liters = \frac{20}{100} \times 40 = 8 liters.Now, the total solution = 40 + 𝑥 liters.New concentration of alcohol:\frac{8}{40 + x} \times 100 = 10Solve for 𝑥: 8 = 0.1 × (40 + 𝑥) ⇒ 8 = 4 + 0.1𝑥 ⇒ 𝑥 = 40 liters.So, 40 liters of water must be added.Question 6: A 20-liter mixture contains milk and water in the ratio 3:1. How much water must be added to make the ratio 1:1?Solution:Amount of milk in the mixture: \frac{3}{4} \times 20 = 15 liters.Amount of water in the mixture: 20 - 15 = 5 liters.Let 𝒙 liters of water be added to make the ratio 1:1Set up the equation: \frac{15}{5 + x} = 1 \Rightarrow 15 = 5 + x \Rightarrow x = 10Therefore, 10 liters of water must be added. Comment More infoAdvertise with us Next Article Algebra Practice Questions Easy Level K kartik Follow Improve Article Tags : Aptitude Similar Reads Aptitude Questions and Answers Aptitude questions can be challenging, but with the right preparation and practice, you can tackle them with ease. Our comprehensive guide to aptitude questions and answers covers all the essential topics of Aptitude, including Quantitative Aptitude, Logical Reasoning, and Verbal Ability. Whether yo 3 min read Quantitative AptitudeWhat are Numbers?Numbers are symbols we use to count, measure, and describe things. 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Data Interpretation questions require the ability to analyze and interpret different forms of data, including tables, graphs, charts, and more. With a focus on percentage, ratio and proportion, data interpretat 8 min read Misc15 Most Important Aptitude Topics For Placements [2025]If you are a student and getting ready for off-campus or on-campus placement, then working on aptitude is quite essential. In many colleges, companies like TCS, Infosys, Capgemini, and Accenture sort students through the mass-hiring process on the basis of aptitude tests. Also, if you are going for 7 min read How to Prepare for Aptitude Test for Campus PlacementsAptitude Tests are used by many recruiters around the world. Their purpose is to test technical skills, attitudes, and soft skills related to the search for a figure to be included in the company. Beyond specific professional skills, Aptitude tests are generally designed to assess a candidate's logi 8 min read Like