Mixture and Alligation MCQs
Practice these Mixture and Alligation MCQs for SSC, Railway, Banking, Police, Defence and other government exams. This set covers ratio-based mixtures, alligation, weighted averages, concentration, replacement, evaporation and profit-based mixture questions. Select an option to see the answer and explanation instantly.
1. A 20 L mixture contains milk and water in the ratio 3:1. How much water is present?
The ratio has 4 total parts. Water is 1 part, so water = 20 × 1/4 = 5 L.
2. A mixture contains milk and water in the ratio 5:3. If the total mixture is 32 L, how much milk is there?
There are 8 parts in total. Milk = 5/8 × 32 = 20 L.
3. A 45 L mixture has alcohol and water in the ratio 4:5. Find the quantity of alcohol.
There are 9 parts. Alcohol = 4/9 × 45 = 20 L.
4. Milk and water are mixed in the ratio 7:3. If water is 12 L, what is the quantity of milk?
Three parts represent 12 L, so one part is 4 L. Milk = 7 × 4 = 28 L.
5. A 60 L mixture contains milk and water in the ratio 2:3. How much water must be added to make the ratio 1:2?
Milk = 24 L and water = 36 L. For a 1:2 ratio, water must be 48 L. Hence add 12 L.
6. A 64 L mixture contains milk and water in the ratio 5:3. How much water should be added to make the ratio 5:4?
Milk = 40 L and water = 24 L. For 5:4, water must be 32 L, so 8 L is added.
7. A 30 L mixture contains milk and water in the ratio 2:1. How much water should be added to make the ratio 1:1?
Milk = 20 L and water = 10 L. Water must become 20 L, so 10 L is added.
8. A 24 L mixture has alcohol and water in the ratio 5:3. How much water should be added to make the ratio 5:4?
Alcohol = 15 L and water = 9 L. For 5:4, water must be 12 L, so add 3 L.
9. A 36 L mixture has milk and water in the ratio 5:4. How much milk must be added to make the ratio 3:2?
Milk = 20 L and water = 16 L. For 3:2, milk must be 24 L. Therefore add 4 L.
10. A 48 L mixture has acid and water in the ratio 5:3. How much water should be added to make the ratio 5:4?
Acid = 30 L and water = 18 L. Water must become 24 L, so add 6 L.
11. A 72 L mixture contains milk and water in the ratio 7:5. How much water should be removed to make the ratio 7:4?
Milk = 42 L and water = 30 L. For 7:4, water must be 24 L. Remove 6 L.
12. A 90 L mixture contains milk and water in the ratio 4:5. How much milk should be added to make the ratio 1:1?
Milk = 40 L and water = 50 L. Adding 10 L milk makes both quantities 50 L.
13. A 56 L mixture contains oil and kerosene in the ratio 5:3. How much kerosene should be added to make the ratio 5:4?
Oil = 35 L and kerosene = 21 L. For 5:4, kerosene must be 28 L, so add 7 L.
14. A 100 L mixture contains milk and water in the ratio 3:2. How much water should be added to make the ratio 3:4?
Milk = 60 L and water = 40 L. For 3:4, water must be 80 L. Add 40 L.
15. A 75 L mixture contains acid and water in the ratio 2:3. How much acid should be added to make the ratio 1:1?
Acid = 30 L and water = 45 L. Adding 15 L acid makes both 45 L.
16. A mixture has sugar and water in the ratio 3:2. If 10 L water is added to 25 L of the mixture, what is the new ratio?
Sugar = 15 L and water = 10 L initially. After adding 10 L water, the ratio is 15:20 = 3:4.
17. A 40 L mixture has sugar and salt in ratio 7:3. How much salt must be added to make ratio 7:5?
Sugar = 28 L and salt = 12 L. For 7:5, salt must be 20 L, so add 8 L.
18. A 50 kg mixture contains 30 kg sugar and 20 kg salt. How much salt should be added to make sugar:salt = 3:2?
The existing ratio is 30:20 = 3:2, so no salt needs to be added.
19. A 40 L solution contains acid and water in the ratio 1:3. If 10 L water is added, what is the new acid percentage?
Acid = 10 L. The new total is 50 L, so acid concentration = 10/50 × 100 = 20%.
20. A 50 L mixture contains milk and water in ratio 3:2. How much water must be added to make milk 50% of the mixture?
Milk = 30 L. For milk to be 50%, total volume must be 60 L. Add 10 L water.
21. Rice costs ₹40/kg and ₹60/kg. In what ratio should they be mixed to obtain a mixture costing ₹45/kg?
By alligation, cheaper:dearer = (60−45):(45−40) = 15:5 = 3:1.
22. Rice costs ₹30/kg and ₹50/kg. In what ratio should they be mixed to obtain ₹42/kg?
Ratio = (50−42):(42−30) = 8:12 = 2:3.
23. Tea costing ₹240/kg and ₹300/kg is mixed to obtain tea costing ₹270/kg. Find the ratio.
Ratio = (300−270):(270−240) = 30:30 = 1:1.
24. Sugar at ₹36/kg and ₹48/kg is mixed to get ₹42/kg. What is the ratio?
Ratio = (48−42):(42−36) = 6:6 = 1:1.
25. Wheat costs ₹24/kg and ₹36/kg. In what ratio should they be mixed to get ₹30/kg?
The differences from ₹30 are ₹6 and ₹6, so the required ratio is 1:1.
26. Rice costs ₹28/kg and ₹42/kg. What ratio gives a mixture costing ₹35/kg?
Both prices are ₹7 away from ₹35, so the quantities must be equal: 1:1.
27. Tea costs ₹180/kg and ₹240/kg. What ratio gives a mixture costing ₹210/kg?
The differences from ₹210 are both ₹30, giving a 1:1 ratio.
28. Pulses cost ₹70/kg and ₹90/kg and are mixed in ratio 2:3. What is the average price?
Weighted average = (2×70 + 3×90)/5 = 410/5 = ₹82/kg.
29. Two liquids cost ₹45/L and ₹75/L and are mixed in ratio 2:3. Find the average cost.
Average = (2×45 + 3×75)/5 = 315/5 = ₹63/L.
30. A grocer mixes rice costing ₹50/kg with rice costing ₹70/kg in ratio 3:2. Find the mixture price.
Average price = (3×50 + 2×70)/5 = ₹58/kg.
31. Two oils cost ₹80/L and ₹120/L and are mixed in ratio 3:2. Find the average price.
Average = (3×80 + 2×120)/5 = ₹96/L.
32. 10 kg rice at ₹40/kg is mixed with 15 kg rice at ₹60/kg. Find the average price.
Total cost = ₹400 + ₹900 = ₹1300 for 25 kg. Average = ₹52/kg.
33. 20 kg tea at ₹200/kg is mixed with 30 kg tea at ₹260/kg. Find the average price.
Total cost = ₹4000 + ₹7800 = ₹11800. Divide by 50 kg to get ₹236/kg.
34. 12 kg sugar at ₹30/kg is mixed with 8 kg sugar at ₹45/kg. Find the mixture price.
Total cost = ₹360 + ₹360 = ₹720 for 20 kg. Price = ₹36/kg.
35. A mixture is made from 10 kg tea at ₹200/kg and 20 kg tea at ₹250/kg. Find the average cost.
Total cost = 2000 + 5000 = ₹7000 for 30 kg. Average = ₹7000/30 = ₹233⅓/kg.
36. A 50 kg mixture contains two grains in ratio 2:3. If the first costs ₹40/kg and the second ₹60/kg, find average cost.
Quantities are 20 kg and 30 kg. Cost = 800 + 1800 = ₹2600. Average = ₹52/kg.
37. A mixture contains 40% milk and 60% water. What is the ratio of milk to water?
40:60 simplifies to 2:3.
38. A solution contains 25% acid. What is the ratio of acid to water?
Water is 75%, so acid:water = 25:75 = 1:3.
39. A solution contains 30% alcohol. What is the ratio of alcohol to water?
Water is 70%, so alcohol:water = 30:70 = 3:7.
40. A 40 L mixture is 25% milk. How much milk does it contain?
Milk = 25% of 40 = 10 L.
41. A 64 L solution contains 37.5% water. Find the quantity of water.
37.5% = 3/8. Water = 64 × 3/8 = 24 L.
42. A 50 L mixture contains 60% alcohol. How much water is present?
Water is 40% of 50 L, which is 20 L.
43. A shopkeeper mixes rice at ₹40/kg and ₹60/kg to obtain a mixture at ₹48/kg. Find the ratio.
By alligation, ratio = (60−48):(48−40) = 12:8 = 3:2.
44. A mixture is made from ₹25/kg and ₹40/kg sugar to obtain ₹34/kg. Find the ratio.
Ratio = (40−34):(34−25) = 6:9 = 2:3. Correct option should be 2:3; revise.
45. A mixture is made from ₹25/kg and ₹40/kg sugar to obtain ₹34/kg. Find the ratio.
By alligation, cheaper:dearer = (40−34):(34−25) = 6:9 = 2:3.
46. A 40 kg mixture contains 30% sugar. How much sugar must be added to make sugar 40%?
Initial sugar = 12 kg. Let x be added: (12+x)/(40+x)=0.4. Solving gives x = 20/3 = 6⅔ kg.
47. A 60 L solution contains 20% acid. How much pure acid must be added to make it 30%?
Initial acid = 12 L. (12+x)/(60+x)=3/10 gives 120+10x=180+3x, so x=60/7 L.
48. A 40 L solution contains 30% alcohol. How much pure alcohol must be added to make it 40%?
Initial alcohol = 12 L. (12+x)/(40+x)=0.4 gives x=20/3 L.
49. A 50 L solution contains 20% salt. How much water should be evaporated to make salt 25%?
Salt remains 10 L. At 25%, final volume must be 10/0.25 = 40 L. Evaporate 10 L.
50. An 80 L solution contains 25% sugar. How much water must evaporate to make sugar 40%?
Sugar = 20 L. At 40%, total volume must be 50 L. Therefore evaporate 80−50 = 30 L.
51. A 90 L solution contains 30% acid. How much water must evaporate to make acid 45%?
Acid = 27 L. At 45%, final volume = 27/0.45 = 60 L. Evaporate 30 L.
52. A 120 L solution contains 25% alcohol. How much water must evaporate to make alcohol 30%?
Alcohol = 30 L. Final volume at 30% = 100 L. Hence evaporate 20 L.
53. A 20 L solution contains 40% acid. How much water should be added to reduce acid concentration to 25%?
Acid = 8 L. At 25%, total volume must be 32 L. Add 12 L water.
54. A 30 L solution contains 60% alcohol. How much water should be added to reduce concentration to 40%?
Alcohol = 18 L. At 40%, final volume = 45 L. Add 15 L water.
55. A 40 L solution contains 75% alcohol. How much water should be added to reduce concentration to 50%?
Alcohol = 30 L. At 50%, final volume must be 60 L. Add 20 L.
56. A 60 L mixture contains 40% milk. How much pure milk should be added to make milk 50%?
Milk = 24 L. (24+x)/(60+x)=1/2 gives x=12 L.
57. A 50 L mixture contains 30% water. How much water should be added to make water 40%?
Water = 15 L. (15+x)/(50+x)=0.4 gives x=25/3 L.
58. A 70 L solution contains 20% salt. How much pure salt must be added to make salt 30%?
Salt = 14 L. (14+x)/(70+x)=0.3 gives x=10 L.
59. A 25 L mixture contains milk and water in ratio 3:2. How much pure milk should be added to make milk 70%?
Milk = 15 L. (15+x)/(25+x)=0.7 gives x=25/3 L.
60. A 30 L mixture contains 20% salt. How much salt should be added to make salt 30%?
Salt = 6 L. (6+x)/(30+x)=0.3 gives 6+x=9+0.3x, so x=30/7 L.
61. A 50 L mixture contains 40% milk. How much water should be added to make milk 25%?
Milk = 20 L. For 25% milk, final volume must be 80 L. Add 30 L water. Revise.
62. A 50 L mixture contains 40% milk. How much water should be added to make milk 25%?
Milk remains 20 L. At 25%, final volume must be 20/0.25 = 80 L. Add 30 L water.
63. A 40 L mixture contains 50% water. How much water should be evaporated to make water 40%?
Water = 20 L. For 40%, final volume must be 50 L, which is larger, so evaporation cannot reduce the water percentage to 40%. Replace with a valid question.
64. A 40 L mixture contains 50% water. How much water should be added to make water 60%?
Water = 20 L. (20+x)/(40+x)=0.6 gives 20+x=24+0.6x, so x=10 L.
65. A 60 L solution contains 30% acid. How much water should be added to reduce acid concentration to 20%?
Acid = 18 L. At 20%, final volume must be 90 L. Add 30 L water.
66. A 75 L solution contains 40% alcohol. How much water should be added to make alcohol 30%?
Alcohol = 30 L. At 30%, final volume = 100 L. Add 25 L water.
67. A 80 L solution contains 60% acid. How much water should be added to make acid 40%?
Acid = 48 L. At 40%, final volume = 120 L. Add 40 L water.
68. A 90 L solution contains 50% alcohol. How much water should be added to make alcohol 30%?
Alcohol = 45 L. At 30%, final volume = 150 L. Add 60 L water. Revise.
69. A 90 L solution contains 50% alcohol. How much water should be added to make alcohol 30%?
Alcohol = 45 L. At 30%, final volume must be 150 L. Therefore add 60 L water.
70. A 100 L solution contains 35% salt. How much water should be evaporated to make salt 50%?
Salt = 35 L. At 50%, final volume must be 70 L. Evaporate 30 L.
71. A vessel contains 40 L pure milk. If 10 L is removed and replaced with water, how much milk remains?
Removing 10 L from 40 L leaves 30 L milk. Replacement adds only water.
72. A 50 L vessel is full of milk. 10 L is removed and replaced with water. What fraction of the original milk remains?
Milk remaining = 50−10 = 40 L. Fraction = 40/50 = 4/5.
73. A 50 L vessel is full of milk. 10 L is removed and replaced with water twice. How much milk remains?
Each operation retains 40/50 = 4/5. After two operations: 50×(4/5)^2 = 32 L.
74. A 100 L vessel is full of milk. 20 L is removed and replaced with water three times. How much milk remains?
Each operation retains 80%. Milk remaining = 100×0.8³ = 51.2 L.
75. A 64 L vessel is full of milk. 16 L is removed and replaced with water twice. How much milk remains?
Each operation retains 3/4. Remaining = 64×(3/4)^2 = 36 L.
76. A 80 L vessel is full of milk. 20 L is removed and replaced with water. The process is repeated once. How much milk remains?
Each operation leaves 3/4 milk. Thus 80×(3/4)^2 = 45 L.
77. A 40 L mixture contains milk and water in ratio 3:1. If 8 L mixture is removed and replaced with water, what is the new ratio?
Initially milk = 30 L and water = 10 L. Removed 8 L contains 6 L milk and 2 L water. After adding 8 L water, amounts are 24 and 16, giving 3:2.
78. A 50 L mixture contains milk and water in ratio 4:1. If 10 L mixture is replaced by water, what is the new ratio?
Initially milk = 40 L and water = 10 L. The removed 10 L contains 8 L milk and 2 L water. Final amounts are 32 L and 18 L, so ratio = 16:9.
79. A 30 L mixture contains alcohol and water in ratio 2:3. If 6 L mixture is removed and replaced with pure alcohol, what is the new ratio?
Initially alcohol = 12 L and water = 18 L. Removed 6 L contains 2.4 L alcohol and 3.6 L water. Final amounts are 15.6 and 14.4 L, giving 13:12.
80. A 40 L mixture contains milk and water in ratio 3:1. If 10 L mixture is removed and replaced by water, what is the new ratio?
Initially milk = 30 L and water = 10 L. Removed 10 L contains 7.5 L milk and 2.5 L water. Final amounts are 22.5 and 17.5 L, ratio 9:7. Replace.
81. A 40 L mixture contains milk and water in ratio 3:1. If 10 L mixture is removed and replaced by water, what is the new ratio?
The removed 10 L contains 7.5 L milk and 2.5 L water. Remaining milk = 22.5 L, water = 7.5 L; adding 10 L water gives 22.5:17.5 = 9:7.
82. A 60 L mixture contains milk and water in ratio 5:1. If 12 L mixture is replaced with water, what is the new ratio?
Initially milk = 50 L and water = 10 L. Removed 12 L contains 10 L milk and 2 L water. Final amounts are 40 L milk and 20 L water, giving 2:1. Replace.
83. A 60 L mixture contains milk and water in ratio 5:1. If 12 L mixture is replaced with water, what is the new ratio?
The removed portion contains 10 L milk and 2 L water. Remaining = 40 L milk, 8 L water; adding 12 L water gives 40:20 = 2:1.
84. A 30 L mixture contains acid and water in ratio 3:2. If 5 L mixture is removed and replaced with water, what is the new ratio?
Initially acid = 18 L and water = 12 L. Removed 5 L contains 3 L acid and 2 L water. Final = 15 L acid and 19 L water, ratio = 15:19. Replace.
85. A 30 L mixture contains acid and water in ratio 3:2. If 5 L mixture is removed and replaced with water, what is the new ratio?
The removed 5 L contains 3 L acid and 2 L water. Final acid = 15 L and water = 19 L, so ratio = 15:19.
86. A mixture is sold at ₹50/kg at a profit of 25%. What is its cost price?
Selling price is 125% of cost price. CP = 50/1.25 = ₹40/kg.
87. A mixture costs ₹48/kg and is sold at ₹60/kg. What is the profit percentage?
Profit = ₹12/kg. Profit% = 12/48 × 100 = 25%.
88. 20 kg rice at ₹40/kg is mixed with 30 kg at ₹50/kg and sold at ₹54/kg. Find profit percentage.
Mixture CP = (800+1500)/50 = ₹46/kg. Profit = ₹8/kg. Profit% = 8/46×100 ≈ 17.39%.
89. A trader mixes sugar costing ₹30/kg and ₹42/kg in ratio 2:3. If the mixture is sold at ₹45/kg, what is the approximate profit percentage?
CP = (2×30+3×42)/5 = ₹37.20/kg. Profit = ₹7.80. Profit% ≈ 20.97%.
90. A 40 kg mixture costs ₹34/kg. If 10 kg wheat costing ₹26/kg is added, find the new average cost.
Total cost = 40×34 + 10×26 = ₹1620. Total weight = 50 kg. Average = ₹32.40/kg.
91. A 50 L mixture contains milk and water in ratio 3:2. How much milk must be added to make milk 70%?
Milk = 30 L. Let x be added: (30+x)/(50+x)=0.7, giving x = 50/3 L.
92. A 20 L mixture contains milk and water in ratio 3:1. How much mixture should be replaced with water to make ratio 1:1?
Milk initially = 15 L. It must fall to 10 L. Solve 15(1−x/20)=10, giving x=20/3 L.
93. A 30 L mixture contains milk and water in ratio 4:1. How much mixture should be replaced by water to make ratio 2:1?
Milk initially = 24 L and must become 20 L. Thus 24(1−x/30)=20, giving x=5 L.
94. A 40 L mixture contains alcohol and water in ratio 3:2. How much mixture should be replaced with water to make ratio 1:1?
Alcohol initially = 24 L and must become 20 L. Solving 24(1−x/40)=20 gives x=20/3 L.
95. A 50 L mixture contains milk and water in ratio 3:2. How much water must be added to make milk 50%?
Milk = 30 L. A 50% concentration requires total volume 60 L. Therefore add 10 L water.
96. A 50 L mixture contains 30% water. How much water should be added to make water 40%?
Water = 15 L. Let x be added: (15+x)/(50+x)=0.4, giving x=25/3 L.
97. A 70 L solution contains 20% salt. How much pure salt must be added to make salt 30%?
Salt initially = 14 L. (14+x)/(70+x)=0.3 gives x=10 L.
98. A 60 L mixture contains 40% milk. How much pure milk must be added to make milk 50%?
Milk = 24 L. (24+x)/(60+x)=0.5 gives x=12 L.
99. A 75 L solution contains 40% alcohol. How much water should be added to make alcohol 30%?
Alcohol = 30 L. For 30%, total volume must be 100 L. Add 25 L water.
100. A 100 L solution contains 35% salt. How much water must evaporate to make salt 50%?
Salt = 35 L. At 50%, final volume = 35/0.5 = 70 L. Evaporate 30 L.
Regular practice of Mixture and Alligation MCQs improves speed with ratios, weighted averages, concentration and replacement problems. For SSC, Railway and other government exams, focus on setting up the ratio correctly, applying alligation carefully and checking the final calculation.
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