Alligation or Mixture Questions

• In a 40 litre mixture of alcohol and water, the ratio of alcohol to water is 5 : 3. If 20% of this mixture is removed and then the same volume is replaced with pure water, what will be the ratio of alcohol to water in the final mixture?
• A sample of lotion has a total volume of 9 ml and contains 50% alcohol by volume. How much water (in ml) must be added to this 9 ml lotion so that the resulting mixture becomes a lotion containing 30% alcohol by volume?
• A 70 litre mixture of fruit juice and water contains 10% water by volume. How many litres of water must be added to this mixture so that the new mixture contains 12.5% water by volume (assuming the total volume increases accordingly)?
• Milk and water are mixed in vessel A in the ratio 4:1 (milk:water). Milk and water are mixed in vessel B in the ratio 3:2 (milk:water). If equal quantities are taken from vessel A and vessel B and poured into vessel C, what will be the final ratio of milk to water in vessel C?
• Two varieties of sugar cost ₹18 per kg and ₹24 per kg. In what ratio (cheaper sugar : costlier sugar) should they be mixed so that the resulting mixture costs ₹20 per kg (assuming no loss and simple weighted average pricing)?
• Three different mixtures contain glucose and alcohol with glucose concentrations of 12%, 35%, and 45% respectively. If 2 litres from the first vessel, 3 litres from the second vessel, and 1 litre from the third vessel are mixed together, what will be the ratio of glucose to alcohol in the new mixture?
• One liquid contains 25% benzene and another liquid contains 30% benzene. A can is filled by mixing 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the resulting mixture (assume parts are by volume and additive).
• Three different milk-water mixtures are available with milk to water ratios of 1:2, 2:3, and 3:4 (milk:water). Equal quantities of each mixture are taken and mixed together. What is the final ratio of water to milk in the resulting mixture?
• Two vessels A and B contain milk and water in the following ratios: Vessel A: 4:3 (milk:water) Vessel B: 2:3 (milk:water) In what ratio should the liquids from vessels A and B be mixed so that the resulting mixture contains equal parts of milk and water (i.e., 50% milk and 50% water)?
• An alloy of copper and bronze weighs 50 g and contains 80% copper by weight. How much pure copper (in grams) should be added to this alloy so that the percentage of copper increases to 90% by weight (assume the added material is 100% copper)?
• Two varieties of wheat cost ₹3.20 per kg and ₹2.90 per kg. In what ratio (cheaper wheat : costlier wheat) should they be mixed so that the resulting mixture is worth exactly ₹3.00 per kg (assume no loss and simple weighted average)?
• A milkman has 20 litres of pure milk. He mixes 5 litres of water (available free of cost) into the 20 litres of milk and sells the entire 25 litre mixture at ₹18 per litre (the cost price per litre of pure milk). What is his percentage profit on the transaction?
• There are two mixtures of honey and water: Mixture 1 has honey:water = 1:3. Mixture 2 has honey:water = 3:1. If 2 litres are taken from mixture 1 and 3 litres are taken from mixture 2 and mixed together, what will be the final ratio of honey to water in the new mixture?
• A petrol tank contains 200 litres of pure petrol. Each time the seller sells 40 litres of petrol (or the current petrol-kerosene mixture), and then immediately replaces the sold 40 litres by adding 40 litres of kerosene back into the tank (so the tank remains 200 litres). After repeating this sell-and-replace process 4 times, how many litres of kerosene will be present in the tank?
• A merchant mixes two varieties of oil costing ₹60 per kg and ₹65 per kg. He wants to sell the resulting mixture at ₹68.20 per kg and make a profit of 10%. In what ratio (₹60 oil : ₹65 oil) should the two oils be mixed (assume profit is calculated on the mixture cost price)?
• A container has 50 litres of milk. A process is repeated three times: (1) Remove 5 litres of the current mixture from the container. (2) Replace the removed 5 litres by adding 5 litres of water. After performing this remove-and-replace process 3 times, how many litres of milk will be left in the container (assume perfect mixing each time)?
• A mixture has a total volume of 240 litres. In this mixture, water is 20% and the remaining 80% is milk. A quantity of the mixture is removed and replaced with pure water (assume perfect mixing). How many litres of the mixture should be removed and replaced so that the percentage of water becomes 40% in the final mixture?
• A container initially contains 120 litres of pure diesel. From the container, 12 litres of the current mixture is removed and replaced with 12 litres of kerosene. This remove-and-replace operation is repeated 3 times in total (assume perfect mixing before each removal). How many litres of diesel will remain in the container after the 3rd replacement?
• Alloy 1 contains gold and silver in the ratio 5:8 (gold:silver). Alloy 2 contains gold and silver in the ratio 5:3 (gold:silver). If equal amounts of alloy 1 and alloy 2 are melted together, what will be the ratio of gold to silver in the resulting alloy?
• In a 100 litre mixture, the ratio of milk to water is 6:4 (milk:water). How many litres of milk must be added to this mixture so that the new ratio of milk to water becomes 3:1 (milk:water), assuming only milk is added and the water quantity remains unchanged?