Quantitative Aptitude

Mixtures and Alligation

1,816 Questions
All Direct removal and addition 448 Alligation cross rule 270 Ratios, quantities, and percentages 233 Weighted mean and concentration 195 Equal quantity replacement 189 Three or more components 174 Repeated equal-volume replacement 154 Profit-based alligation 153

Mixtures and Alligation Questions

Multiple choice

Bottle 1 contains a mixture of milk andwater in 7: 2 ratio and Bottle 2 contains amixture of milk and water in 9: 4 ratio. Inwhat ratio of volumes should the liquids inBottle 1 and Bottle 2 be combined toobtain a mixture of milk and water in 3:1ratio?

  1. 24:13

  2. 27:13

  3. 27:16

  4. 23:18

  5. 27:14
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using alligation on milk: Bottle 1 has 7/9 milk, Bottle 2 has 9/13 milk, target is 3/4. (3/4 - 9/13) / (7/9 - 3/4) = (39-36)/52 / (28-27)/36 = (3/52) / (1/36) = 108/52 = 27/13.

Multiple choice

Quantity I: A milkman has 45 liters mixture of milk and water in the ratio of 5: 4. If 10 liters water is added, then what is percentage of water in the final mixture? Quantity II: A vessel contains 40 liters mixture of water and acid in the ratio of 3: 2. If 20 liters of mixture is taken out and replaced by water, then what percentage of acid in the final mixture?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: 45L, 5:4 ratio. Milk = 25, Water = 20. Add 10L water: Water = 30, Total = 55. %Water = 30/55 = 54.54%. Quantity II: 40L, 3:2 ratio. Water = 24, Acid = 16. Remove 20L mixture (12 water, 8 acid). Remaining: 12 water, 8 acid. Add 20L water: Total water = 32, Total acid = 8, Total volume = 40. %Acid = 8/40 = 20%. Quantity I > Quantity II.

Multiple choice

A container has a mixture of two liquids A and B in the ratio 4 : 1. When 5 liters of the mixture is removed and replaced with 5 liters of liquid B, the ratio becomes 2 : 3. Find the initial quantities of liquids A and B in the mixture.

  1. 8 liters and 2 liters

  2. 10 liters and 5 liters

  3. 12 liters and 3 liters

  4. 16 liters and 4 liters

  5. 20 liters and 5 liters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial ratio 4:1. Let A=4x, B=x. Removing 5L removes 4L of A and 1L of B. Remaining: A=4x-4, B=x-1. Adding 5L of B: A=4x-4, B=x+4. Ratio (4x-4)/(x+4) = 2/3. 12x-12 = 2x+8 => 10x=20 => x=2. A=8, B=2.

Multiple choice

In a garden, a fertilizer mixture consists of two types, A and B, in a container with a total volume of 110 liters. The initial ratio of fertilizer A to fertilizer B is 4 : 7. After adding some amount of fertilizer B, the new ratio becomes 4 : 9. What is the amount of fertilizer B added?

  1. 2 liters

  2. 3 liters

  3. 10 liters

  4. 20 liters

  5. 12.5 liters
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial: A = 40, B = 70 (Total 110). New ratio A:B = 4:9. Since A remains 40, 4 units = 40, so 1 unit = 10. New B = 9 * 10 = 90. Added B = 90 - 70 = 20.

Multiple choice

A vessel of 160 L is filled with milk and water. 70% of milk and 30% of water is taken out of the vessel. It is found out that the vessel is vacated by 55%, then the quantity of milk and water in the original mixture is

  1. Milk = 100 L; Water = 60 L

  2. Milk = 60 L; Water = 100 L

  3. Milk = 90 L; Water = 70 L

  4. Milk = 70 L; Water = 90 L
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M be milk and W be water. We have M + W = 160. The problem states 0.7M + 0.3W = 0.55 * 160 = 88. Solving the system 0.7M + 0.3(160 - M) = 88 leads to 0.4M = 40, so M = 100 and W = 60.

Multiple choice

A receptacle is filled to a capacity of 75% and it contains a mixture of 50% orange juice, 25% apple juice and rest is water. The remaining portion of the receptacle is filled with 90 mL of lemonade. How much orange juice is present in the receptacle?

  1. 120 mL

  2. 130 mL

  3. 135 mL

  4. 140 mL

  5. 145 mL
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Receptacle is 75% full. The remaining 25% is 90 mL, so total capacity is 360 mL. The 75% filled portion is 270 mL. This 270 mL is 50% orange juice, so 0.5 * 270 = 135 mL.

Multiple choice

A cleaning solution contains 30% vinegar and rest water. If 20% of the solution is substituted with water and this procedure is repeated two more times, what will be the approximate vinegar concentration in the final cleaning solution?

  1. 5%

  2. 12%

  3. 15%

  4. 18%

  5. 21%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The vinegar concentration starts at 30%. Each substitution of 20% of the solution with water reduces the vinegar content by 20% (multiplying by 0.8). After three cycles, the concentration is 30% * (0.8)^3 = 30% * 0.512 = 15.36%, which is approximately 15%.

Multiple choice

In a nutrition research facility, scientists are experimenting with five distinct protein solutions. Solution A contains 8% protein by weight, solution B consists of 12% protein, solution C is made up of 15% protein, solution D comprises 20% protein, and solution E contains 25% protein. If the researchers mix 10 pounds of solution A, 15 pounds of solution B, 20 pounds of solution C, 25 pounds of solution D, and 30 pounds of solution E, which of the following choices gives the best approximation for the resulting mixture's percentage of protein?

  1. 18%

  2. 22%

  3. 28%

  4. 30%

  5. 32%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total protein = (10*0.08) + (15*0.12) + (20*0.15) + (25*0.20) + (30*0.25) = 0.8 + 1.8 + 3 + 5 + 7.5 = 18.1 lbs. Total weight = 10+15+20+25+30 = 100 lbs. Percentage = 18.1/100 = 18.1%.

Multiple choice

Lisa is making a mixture by combining two vinegar solutions. The first solution has 3 liters with a 25% concentration, and the second solution has 6 liters with a stronger concentration. After mixing, she gets 9 liters of a solution with a 40% concentration. What percentage concentration did the second solution originally have?

  1. 35.7%

  2. 45.5%

  3. 47.5%

  4. 55.8%

  5. 75.5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total volume = 9L. Total vinegar = 40% of 9 = 3.6L. First solution: 25% of 3L = 0.75L. Second solution: 3.6 - 0.75 = 2.85L. Concentration = 2.85 / 6 = 0.475 = 47.5%.

Multiple choice

A milk vendor has two cans – C1 and C2 – of capacity of 300 litres each. Both the cans are full to the brim with milk-water solution. The concentration of milk in C1 is 75% and that in C2 is 50%. How much quantity of solution should the vendor mix from the C1 and C2 such that he gets 180 litres of solution having water and milk in the ratio of 3:5?

  1. 90 litres, 90 litres

  2. 72 litres, 108 litres

  3. 45 litres, 135 litres

  4. 40 litres, 140 litres
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

C1 has 75% milk (25% water), C2 has 50% milk (50% water). We want 180L with 5/8 milk (62.5%) and 3/8 water (37.5%). Using allegation: (75 - 62.5) : (62.5 - 50) = 12.5 : 12.5 = 1:1. Thus, equal parts of 90L each are needed.