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

There are 4 bottles of equal volume containing sugar solution. Each bottle is filled at least up to 40% of its capacity. The concentrations of the solutions in the four bottles are 20%, 30%, 50%, and 70%, respectively. If the solutions of these four bottles are emptied into a large container and mixed properly, what can be the minimum and maximum concentration of sugar in the resulting mixture?

  1. Minimum = 32.0%, Maximum = 57.5%

  2. Minimum = 35.0%, Maximum = 50.0%

  3. Minimum = 36.5%, Maximum = 60.0%

  4. Minimum = 37.5%, Maximum = 52.5%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The mixture concentration depends on the volume of each solution. Since each bottle is at least 40% full, the total volume is between 1.6 and 4.0 units. The weighted average of concentrations (20, 30, 50, 70) will be minimized when the lower concentration bottles are at maximum capacity and maximized when the higher concentration bottles are at maximum capacity.

Multiple choice

A mixture is made of two kinds of chemicals. The chemicals are in the ratio 3 : 2. Another mixture is made of the same two chemicals, but in this, the chemicals are in the ratio 4 : 5. How much quantity of the other mixture must be mixed with 3 L of the former mixture so that the resulting mixture may contain equal quantities of both the chemicals?

  1. 5 2 5 L

  2. 5 2 3 L

  3. 4 1 2 L

  4. 3 3 4 L

  5. 2 1 3 L
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In 3 L of the first mixture, the quantities are 1.8 L and 1.2 L. If x litres of the second mixture are added, its quantities are 4x/9 and 5x/9; equating the final quantities gives x = 5.4 L, or 5 2/5 L.

Multiple choice

A cane contains a mixture of two liquids, 'A' and 'B' in the ratio 7 : 5. When 9 liters of mixture are drawn off and the cane is filled with 'B', the ratio of 'A' and 'B' becomes 7 : 9 liters. How many liters of Liquid 'A' was initially contained by the cane?

  1. 15.25

  2. 18

  3. 21

  4. 17.5

  5. 16.75
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the initial quantity be V litres. After removing 9 litres, the amount of A is 7(V - 9)/12, and the final ratio makes it 7V/16. Equating these gives V = 36 litres, so the initial amount of A is 7/12 × 36 = 21 litres.

Multiple choice

Two glasses contain mixtures of alcohol and water in the ratios 2 : 1 and 1 : 1. The mixtures are poured into a third glass in equal quantities. What is the ratio of alcohol to water in the final mixture?

  1. 5 : 7

  2. 7 : 5

  3. 7 : 6

  4. 6 : 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Glass 1 has 2/3 alcohol and 1/3 water. Glass 2 has 1/2 alcohol and 1/2 water. Combining equal parts, the alcohol ratio is (2/3 + 1/2) / 2 = 7/12, and the water ratio is (1/3 + 1/2) / 2 = 5/12. The resulting ratio is 7:5.

Multiple choice

A container holds 200 litres of a solution of acid and water, having 30% acid by volume. Atul replaces 20% of this solution with water, then replaces 10% of the resulting solution with acid, and finally replaces 15% of the solution thus obtained, with water. The percentage of acid by volume in the final solution obtained after these three replacements, is nearest to

  1. 25

  2. 27

  3. 29

  4. 23
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Start: 60 acid, 140 water. 1. Replace 20% (40L) with water: 40L removed (12 acid, 28 water). Remaining: 48 acid, 112 water. Add 40L water: 48 acid, 152 water. 2. Replace 10% (20L) with acid: 20L removed (4.8 acid, 15.2 water). Remaining: 43.2 acid, 136.8 water. Add 20L acid: 63.2 acid, 136.8 water. 3. Replace 15% (30L) with water: 30L removed (9.48 acid, 20.52 water). Remaining: 53.72 acid, 146.28 water. Add 30L water: 53.72 acid, 146.28 water. Final % = 53.72 / 200 = 26.86%. Nearest is 27.

Multiple choice

The ratio of alcohol to water in two containers, A and B, are 5 : 3 and 1 : 3, respectively, with both containers having infinite capacity. Suppose that the aim is to obtain 2.1 litre of liquid which is composed of equal quantities of alcohol and water. How much liquid should be drawn from A?

  1. 1.4 litre

  2. 1.05 litre

  3. 0.35 litre

  4. 1.1 litre
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the amount from A and y be the amount from B. x + y = 2.1. Alcohol content: (5/8)x + (1/4)y = 1.05. Substitute y = 2.1 - x: (5/8)x + (1/4)(2.1 - x) = 1.05. (5/8 - 2/8)x = 1.05 - 0.525. (3/8)x = 0.525. x = 0.525 * 8 / 3 = 1.4.

Multiple choice

A laboratory tank holds 300 litres of a solution of reagent and water, having 40% reagent by volume. A technician drains 50% of this solution and replaces it with water, then drains 25% of the resulting solution and replaces it with pure reagent. Finally, he drains 25% of the solution thus obtained and replaces it with water. The percentage of reagent by volume in the final solution obtained after these three replacements is:

  1. 26%

  2. 28%

  3. 30%

  4. 32%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Start: 300L, 120L reagent (40%). 1) Drain 50% (150L left, 60L reagent), add 150L water: 60L reagent. 2) Drain 25% (112.5L left, 45L reagent), add 75L pure reagent: 45+75 = 120L reagent. 3) Drain 25% (225L left, 90L reagent), add 75L water: 90L reagent. Final % = 90/300 = 30%.