MCQ
Numerical: Mixtures & Alligation MCQ - Practice Questions with Answers
Solve 15 Numerical: Mixtures & Alligation questions for RAS/RPSC preparation.
Practice questions
Q1For the following three cases, choose the correct ratios respectively: 1. Milk at ₹40 per litre mixed with water to get an average cost of ₹30 per litre, ratio milk:water. 2. Tea at ₹60 per kg and ₹40 per kg mixed to get ₹48 per kg, ratio dearer:cheaper. 3. Sugar at ₹36 per kg and ₹48 per kg mixed to get ₹42 per kg, ratio cheaper:dearer.
Use alligation: cheaper quantity : dearer quantity = (dearer price − mean price) : (mean price − cheaper price). Case 1: water costs ₹0 and milk costs ₹40; water:milk = (40 − 30):(30 − 0) = 10:30 = 1:3, so milk:water = 3:1. Case 2: dearer:cheaper = (48 − 40):(60 − 48) = 8:12 = 2:3. Case 3: cheaper:dearer = (48 − 42):(42 − 36) = 6:6 = 1:1. Therefore, the required sequence is 3:1, 2:3, 1:1.
Q2Assertion: A 12-litre mixture has milk and water in the ratio 7:5. If 3 litres of water is added, the percentage of milk in the new mixture becomes 46 2/3%. Reason: The milk remains 7 litres and the new total quantity becomes 15 litres, so the milk percentage is (7/15) × 100.
In the original 12-litre mixture, milk : water = 7:5, so milk = 12 × 7/12 = 7 litres and water = 5 litres. After adding 3 litres of water, the milk remains 7 litres, while water becomes 8 litres. The new total quantity is 7 + 8 = 15 litres. Therefore, milk percentage = (7/15) × 100 = 700/15 = 46 2/3%. Thus the assertion is true. The reason gives the same calculation and correctly explains why the assertion is true.
Q3A container has 40 litres of milk. 10 litres are taken out and replaced with water. What is the ratio of milk to water in the final mixture?
Initially the container has 40 litres of pure milk. When 10 litres are removed, the milk left is 40 − 10 = 30 litres. The same 10 litres are then replaced with water, so water in the final mixture is 10 litres. Therefore, milk : water = 30 : 10. Dividing both terms by 10 gives 3 : 1. Hence the final ratio of milk to water is 3 : 1.
Q4A 30% acid solution and a 50% acid solution are mixed to obtain a 42% acid solution. Consider the statements: 1. The required ratio of 30% solution to 50% solution is 2 : 3. 2. The required ratio of 30% solution to 50% solution is 3 : 2. 3. The 50% solution forms 60% of the final mixture. Which statements are correct?
By alligation, the ratio of the 30% solution to the 50% solution is (50 − 42) : (42 − 30) = 8 : 12 = 2 : 3. So statement 1 is correct and statement 2 is wrong. The total parts are 2 + 3 = 5. The 50% solution contributes 3 parts out of 5, so its share is 3/5 × 100 = 60%. Therefore, statements 1 and 3 are correct.
Q5A vessel contains 32 litres of a milk-water mixture in the ratio 5:3. How many litres of water should be added so that the ratio of milk to water becomes 5:7?
In 32 litres of mixture, milk = 32 × 5/8 = 20 litres and water = 32 × 3/8 = 12 litres. Only water is added, so milk remains 20 litres. Let the added water be x litres. New water quantity = 12 + x. Required ratio is 5:7, so 20 : (12 + x) = 5 : 7. Hence 20 × 7 = 5(12 + x), or 140 = 60 + 5x. Therefore x = 16 litres. So, 16 litres of water must be added.
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More questions
6Tea costing ₹180 per kg is mixed with tea costing ₹240 per kg in the ratio 3 : 2. Which of the following statements is correct about the cost price of the mixture?
7A 20% acid solution and a 50% acid solution are to be mixed to obtain a 30% acid solution. Which ratio of the 20% solution to the 50% solution is correct?
8A container has 60 litres of a solution containing 25% alcohol. How many litres of this solution should be removed and replaced with pure alcohol so that the final solution contains 40% alcohol?
9A container has 60 litres of pure milk. 15 litres of milk is taken out and replaced with water. This operation is repeated once more. How many litres of milk will remain in the container?
10A shopkeeper mixes 30 litres of oil costing ₹60 per litre with 20 litres of oil costing ₹85 per litre. Which of the following statements is incorrect?
11Rice costing ₹42 per kg is mixed with rice costing ₹54 per kg. In what ratio should they be mixed so that the mixture costs ₹46 per kg?
12A vessel contains 40 litres of milk and 10 litres of water. If 10 litres of the mixture is taken out and replaced with 10 litres of water, how many litres of milk will remain in the vessel?
13Match each mixing case with the required ratio of the lower-priced or lower-strength item to the higher-priced or higher-strength item. Case 1: ₹30 and ₹52 to get ₹36. Case 2: ₹18 and ₹33 to get ₹24. Case 3: 40% and 75% to get 55%.
14Match the following mixtures with the ratio in which the cheaper item and the dearer item must be mixed. P. ₹20 per kg and ₹32 per kg to get ₹27 per kg. Q. ₹36 per kg and ₹48 per kg to get ₹42 per kg. R. ₹60 per kg and ₹75 per kg to get ₹69 per kg.
1520 litres of a solution containing 30% acid is mixed with 30 litres of another solution containing 50% acid. Which of the following statements is correct?