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

In a chemistry lab, there are two beakers, A and B, each containing a unique chemical solution. Beaker A holds a solution where chemicals X and Y are mixed in the ratio of 3 : 2, while beaker B contains a solution where chemicals X and Y are mixed in the ratio of 4 : 3. The chemist wants to create a new solution by combining these two solutions in a specific ratio. Find the ratio in which the solutions from beakers A and B should be mixed to create a new solution containing chemicals X and Y in the ratio of 7 : 5.

  1. 7 : 5

  2. 5 : 7

  3. 2 : 7

  4. 7 : 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Beaker A: 3/5 X, 2/5 Y. Beaker B: 4/7 X, 3/7 Y. Target: 7/12 X, 5/12 Y. Using alligation on X: |4/7 - 7/12| : |7/12 - 3/5| = |48/84 - 49/84| : |35/60 - 36/60| = 1/84 : 1/60 = 60:84 = 5:7.

Multiple choice

A container contains a 25 L mixture of water and chemical in the ratio of 4 to 1. Extra water and chemical is added to the container, and the ratio becomes 5 : 2. If in this new mixture, the quantity of water added was 15 L more than the chemical added, then what is the quantity of chemical added to the new mixture?

  1. 15 L

  2. 18 L

  3. 30 L

  4. 35 L

  5. 45 L
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial mixture: 20L water, 5L chemical. Let added water be W and chemical be C. We have W = C + 15. The new ratio is (20+W)/(5+C) = 5/2. Substituting W, (20+C+15)/(5+C) = 5/2, so (35+C)/(5+C) = 2.5. Solving 35+C = 12.5 + 2.5C gives 1.5C = 22.5, so C = 15.

Multiple choice

Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce, making a profit of 20 percent. What was the ratio of the mixture?

  1. 1:10

  2. 1:5

  3. 2:7

  4. 3:8

  5. 5:7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Selling price is 7 cents/oz with 20% profit, so cost price = 7 / 1.2 = 5.833 cents/oz. Using alligation: (6 - 5.833) / (5.833 - 5) = 0.167 / 0.833 = 1/5.

Multiple choice

A chemist has two alcohol solutions, one containing 40% alcohol and the other containing 60% alcohol. How much of each should be mixed to get 100 litres of a 50% alcohol solution?

  1. 60 litres of solution having 40% alcohol and 40 litres of solution having 60% alcohol

  2. 50 litres of each solution

  3. 40 litres solution having 40% alcohol and 60 litres of solution having 60% alcohol

  4. 70 litres of solution having 40% alcohol and 30 litres of solution having 60% alcohol

  5. 30 litres of solution having 40% alcohol and 70 litres of solution having 60% alcohol
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the allegation rule or a system of equations: 0.4x + 0.6(100-x) = 0.5(100). 0.4x + 60 - 0.6x = 50. -0.2x = -10. x = 50. Thus, 50 liters of each solution are needed.

Multiple choice

Eight litres are drawn off from a barrel full of milk and then replaced with water. The process is repeated twice. If the final ratio of milk to water in the barrel is 16 : 9, what is volume of the barrel?

  1. 30 litres

  2. 40 litres

  3. 50 litres

  4. 60 litres

  5. 70 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let V be the volume. After 3 operations, milk remaining = V * (1 - 8/V)^3. Ratio of milk to total = 16/25. (1 - 8/V)^3 = 16/25 is not correct; the ratio of milk to water is 16:9, so milk to total is 16/25. (1 - 8/V)^3 = 16/25. (1 - 8/V) = (16/25)^(1/3) = 4/5. 1 - 8/V = 0.8, so 8/V = 0.2, V = 40.

Multiple choice

In a mixture composed of acid and water, where for every 5 litres of acid in the mixture, there is 1 litre of water. If 3 litres of water is added to the mixture, the new mixture contains twice as much acid as water. Find the quantity of acid in the original mixture.

  1. 8 litres

  2. 10 litres

  3. 12 litres

  4. 15 litres

  5. 20 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original ratio of acid to water is 5:1. Let acid = 5x, water = x. After adding 3L water, the ratio is 5x / (x + 3) = 2 / 1. Solving 5x = 2x + 6, we get 3x = 6, so x = 2. Original acid = 5 * 2 = 10 litres.

Multiple choice

A restaurant blends two sauces: one contains 25% chili, while the other contains 55% chili. If 8 litres of the first sauce are mixed with a certain quantity of the second sauce to produce a mixture that is 45% chili, how many litres of the second sauce are required?

  1. 13

  2. 16

  3. 18

  4. 21

  5. 23
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the quantity of the second sauce. The total chili content is 0.25(8) + 0.55(x) = 0.45(8 + x). Solving this gives 2 + 0.55x = 3.6 + 0.45x, so 0.10x = 1.6, which means x = 16.

Multiple choice

Two containers, A and B, have mixtures of chocolate and vanilla. Container A has a mixture in the ratio 2 : 3, and container B has a mixture in the ratio 4 : 5. How many kg of the mixture should be taken from each container to get a final mixture containing 8 kg of chocolate and 11 kg of vanilla?

  1. 9 kg from A and 20 kg from B

  2. 11 kg from A and 9 kg from B

  3. 10 kg from A and 9 kg from B

  4. 9 kg from A and 12 kg from B

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be kg from A and y be kg from B. Chocolate: (2/5)x + (4/9)y = 8. Vanilla: (3/5)x + (5/9)y = 11. Solving the system: 18x + 20y = 360 and 27x + 25y = 495. Multiplying first by 5 and second by 4: 90x + 100y = 1800 and 108x + 100y = 1980. 18x = 180, x = 10. Then 180 + 20y = 360, 20y = 180, y = 9.

Multiple choice

Two containers have mixtures of juice and water in the ratios 4 : 3 and 7 : 6, respectively. In what ratio should the contents be mixed so that the ratio of juice to water in the final mixture is 5 : 4?

  1. 14 : 13

  2. 13 : 14

  3. 11 : 14

  4. 14 : 11

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use the allegation method. Container 1 has 4/7 juice, Container 2 has 7/13 juice, and the mixture has 5/9 juice. The difference between 4/7 and 5/9 is 1/63. The difference between 7/13 and 5/9 is 2/117. The ratio is (2/117) : (1/63) = 14:13.

Multiple choice

Four jars, P, Q, R, and S, contain mixtures of olive oil and vinegar in the ratios of 2 : 3, 5 : 7, 4 : 9, and 3 : 4, respectively. The capacities of the jars are in the ratio of 5 : 12 : 13 : 7. If the contents of all four jars are combined, what is the ratio of olive oil to vinegar in the resulting mixture?

  1. 7 : 17

  2. 4 : 9

  3. 14 : 23

  4. 14 : 27

  5. 17 : 27
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total ratio = (Sum of olive oil) / (Sum of vinegar). Olive oil = 5*(2/5) + 12*(5/12) + 13*(4/13) + 7*(3/7) = 2 + 5 + 4 + 3 = 14. Vinegar = 5*(3/5) + 12*(7/12) + 13*(9/13) + 7*(4/7) = 3 + 7 + 9 + 4 = 23. Ratio = 14:23.