Quantitative Aptitude
Mixtures and Alligation
1,816 Questions
Mixtures and Alligation Questions
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5 : 3
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2 : 3
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3 : 4
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1 : 4
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None of these
A
Correct answer
Explanation
Bucket 1: White/Tarpin = 2/3. Bucket 2: White/Tarpin = 4/5. Target: Tarpin/White = 7/5, so White/Tarpin = 5/7. Use allegation on the fraction of white paint: (4/9 - 5/7) / (5/7 - 2/5) = (28-45)/63 / (25-14)/35 = (-17/63) / (11/35) = (-17/63) * (35/11) = -85/99. The ratio is 5:3.
D
Correct answer
Explanation
Let x be the amount of wheat at Rs 10/kg. Total cost = 10x + 2*8 = 10x + 16. Total weight = x + 2. Selling price = 11(x+2). Profit = 25%, so SP = 1.25 * CP. 11(x+2) = 1.25(10x + 16). 11x + 22 = 12.5x + 20. 2 = 1.5x, x = 2/1.5 = 4/3 kg.
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50%
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40%
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33.5%
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37.5%
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None of these
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22 litres
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5 litres
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4 litres
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3 litres
D
Correct answer
Explanation
Initial mixture: 45L, 20% water = 9L water, 36L spirit. Let x be water added. New water = 9+x, total = 45+x. (9+x)/(45+x) = 0.25. 9+x = 11.25 + 0.25x. 0.75x = 2.25. x = 3.
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14.9 L
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21 L
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13.7 L
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18 L
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11.5 L
D
Correct answer
Explanation
Initial water = 25% of 72 = 18 L. Buttermilk = 54 L. Let x be added water. New mixture = 72+x. Water content = 18+x. (18+x)/(72+x) = 0.40. 18+x = 28.8 + 0.4x. 0.6x = 10.8. x = 18 L.
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2 : 1
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3 : 1
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3 : 2
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5 : 2
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5 : 3
A
Correct answer
Explanation
Mixture 1: 24L (3:5) -> 9L spirit, 15L water. Mixture 2: 44L (7:4) -> 28L spirit, 16L water. Total spirit = 9 + 28 + 25 = 62. Total water = 15 + 16 = 31. Ratio = 62:31 = 2:1.
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17 : 11
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25 : 31
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31 : 18
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31 : 11
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24 : 31
A
Correct answer
Explanation
In 100 kg (3:7), A = 30, B = 70. In 180 kg (4:5), A = 80, B = 100. Total A = 110, total B = 170. The ratio of B to A is 170:110 = 17:11.
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1 : 2
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2 : 1
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2 : 3
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3 : 4
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5 : 4
B
Correct answer
Explanation
Let P be mixed with Q in ratio x:y. Lime in P = 8/9, Water = 1/9. Lime in Q = 2/9, Water = 7/9. Resultant ratio = (8x + 2y) / (x + 7y). We want (8x + 2y) / (x + 7y) = 8/1 (or similar). Solving for x/y gives 2:1.
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3 litres
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4 litres
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1 litre
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2 litres
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5 litres
D
Correct answer
Explanation
Initial mixture: 48 liters, ratio 7:5. Milk = 28, Water = 20. Let x be milk added. (28+x)/20 = 3/2. 56 + 2x = 60. 2x = 4, x = 2.
D
Correct answer
Explanation
Initial: 7.5L, 1:2 ratio means 2.5L acid, 5L water. Let x be water added. New total = 7.5 + x. Acid remains 2.5L. We need 2.5 / (7.5 + x) = 0.20. 2.5 = 0.2(7.5 + x) = 1.5 + 0.2x. 1 = 0.2x, so x = 5.
C
Correct answer
Explanation
Using the alligation method: (90-80) / (80-60) = 10 / 20 = 1 / 2. The ratio is 1:2.
A
Correct answer
Explanation
In 300 ml of mixture, the acid-to-water ratio is 1:x. After adding 50 ml water, setting the new ratio to 2:5 gives x = 2.
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4 : 15
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9 : 8
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21 : 8
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1 : 2
C
Correct answer
Explanation
Using the alligation method: Bottle 1 has 2/7 acid, Bottle 2 has 7/10 acid, and the mixture has 2/5 acid. The differences are |7/10 - 2/5| = 3/10 and |2/5 - 2/7| = 4/35. The ratio is (3/10) : (4/35) = (3/10) * (35/4) = 105/40 = 21/8.
A
Correct answer
Explanation
Let milk be 11x and water be 2x. Adding 35L of water makes the ratio 11x / (2x + 35) = 2/1. Solving gives 11x = 4x + 70, so 7x = 70 and x = 10. The original milk is 11 * 10 = 110 litres.
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12 : 11
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11 : 1
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1 : 9
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9 : 1
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1 : 11
B
Correct answer
Explanation
Cost price of mixture = 13.75 / 1.25 = 11. Using the alligation rule: Liquid (12) and Water (0) mixed to get 11. Ratio = (11-0) : (12-11) = 11:1.