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

A container contains a mixture of Spirit and Water in the ratio 3 : 1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of Spirit and Water of the resultant mixture in the container becomes 1 : 1?

  1. 1/3

  2. 2/3

  3. 3/4

  4. 4/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial ratio 3:1 (Spirit:Water). Let total volume be 4 units (3 spirit, 1 water). Removing fraction 'f' leaves 3(1-f) spirit and 1(1-f) water. Adding 'f' of water makes spirit 3(1-f) and water 1(1-f) + 4f. Set 3(1-f) = 1(1-f) + 4f. 3 - 3f = 1 - f + 4f. 2 = 6f. f = 1/3.

Multiple choice

Spirit and Water are mixed in a vessel A in the ratio of 5 : 2 and in the vessel B in the ratio 8 : 5. In what proportion should quantities be taken out from the two vessels so as to form a mixture in which Spirit and Water will be in the ratio of 9 : 4?

  1. 2 : 3

  2. 2 : 7

  3. 7 : 4

  4. 7 : 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the rule of alligation on the spirit content: Vessel A has 5/7, Vessel B has 8/13, and the target is 9/13. The differences are |8/13 - 9/13| = 1/13 and |5/7 - 9/13| = (65-63)/91 = 2/91. Ratio = (1/13) : (2/91) = 7/91 : 2/91 = 7:2.

Multiple choice

In the first alloy, Aluminium and Tin are in the ratio 1 : 2. In the second alloy the same elements are in the ratio 2 : 3. If these two alloys be mixed to form a new alloy in which two elements are in the ratio 5 : 8, the ratio of these two alloys in the new alloy is

  1. 3 : 10

  2. 3 : 7

  3. 10 : 3

  4. 7 : 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the alligation rule: Alloy 1 (1/3 Al), Alloy 2 (2/5 Al), Target (5/13 Al). (2/5 - 5/13) : (5/13 - 1/3) = (26-25)/65 : (15-13)/39 = 1/65 : 2/39 = 3/195 : 10/195 = 3:10.

Multiple choice

8 litres are drawn from a container full of Milk and is then filled with water. This operation is performed three more times. The ratio of the quantity of Milk now left in the container to that of water is 16 : 65. How much Milk did the container hold originally?

  1. 16 L

  2. 20 L

  3. 24 L

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

Let the original quantity be x. After 4 operations, the remaining milk is x * (1 - 8/x)^4. The ratio of milk to water is 16:65, meaning milk is 16/(16+65) = 16/81 of the total. Thus, (1 - 8/x)^4 = 16/81 = (2/3)^4. Solving 1 - 8/x = 2/3 gives 8/x = 1/3, so x = 24.

Multiple choice

A yellow glass has pineapple juice and red glass has cranberry juice both of equal volumes. 150 ml from yellow glass is taken and poured into the red glass and thoroughly mixed. 150 ml from the red glass is poured into the yellow glass and mixed. This process is repeated 3 more times. Find the ratio of pineapple juice in yellow glass to cranberry juice in red glass.

  1. 1 : 2

  2. 2 : 1

  3. 1 : 3

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is a classic mixture problem. Since the volumes are equal and the exchange is equal, the concentration of pineapple juice in the yellow glass will eventually equal the concentration of cranberry juice in the red glass due to symmetry.

Multiple choice

2gm of steam condenses when passed through 40gm of water initially at 25°C. If the latent heat of vaporization of water is 540kcal/kg, what is the final temperature of the mixture?

  1. 54.3°

  2. 36.1°

  3. 68.2°

  4. 100°
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Heat released by 2g steam condensing: 2g * 540 cal/g = 1080 cal. Heat absorbed by 40g water to reach T: 40g * 1 * (T - 25). Heat released by 2g water cooling from 100 to T: 2g * 1 * (100 - T). Total heat equation: 1080 + 2(100 - T) = 40(T - 25). 1080 + 200 - 2T = 40T - 1000. 2280 = 42T. T = 2280 / 42 = 54.28.

Multiple choice

Hydrochloric acid solutions A and B have concentrations 0.5 N and 0.1N respectively. The volume of solution A and Brequired to make 2 liters of 0.2N Hydrochloric acid are

  1. 0.5 L of A+1.5 L of B

  2. 1.5 L of A+0.5 L of B

  3. 1.0 L of A +1.0 L of B

  4. 0.75 L of A + 1.25 L of B
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the mixture formula V1C1 + V2C2 = V_total * C_total: 0.5x + 0.1(2-x) = 2 * 0.2. 0.5x + 0.2 - 0.1x = 0.4. 0.4x = 0.2. x = 0.5 L of A. Then B = 1.5 L.

Multiple choice

20 L of pure water was added to a vessel containing 80 L of pure milk. 36 L of the resultant mixture was then sold and some more pure milk and pure water was added to the vessel in the respective ratio of 7 : 2. If the final quantity of water was 3 L less than the initial quantity of water in the vessel, what was the quantity of pure milk that was added to the vessel? (in L)

  1. 15.4

  2. 14.7

  3. 13.9

  4. 16.8

  5. 16.1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial water = 20L. After selling 36L of the 100L mixture (80 milk, 20 water), 64L remains (51.2 milk, 12.8 water). Let x be the amount of milk added and (2/7)x be the water added. Final water = 12.8 + (2/7)x = 20 - 3 = 17. Solving for x: (2/7)x = 4.2, so x = 14.7.

Multiple choice

A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it and replaced by the same quantity of liquid B. Again, 4 litres of the mixture is taken out and replaced by the same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?

  1. 4 : 1

  2. 5 : 1

  3. 16 : 9

  4. 17 : 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial volume = 20. After two replacements of 4L (which is 1/5 of the total), the amount of A remaining is 20 * (1 - 4/20)^2 = 20 * (0.8)^2 = 20 * 0.64 = 12.8. Amount of B = 20 - 12.8 = 7.2. Ratio A:B = 12.8 : 7.2 = 128 : 72 = 16 : 9.

Multiple choice

A container contains 'X' litres of milk. A thief stole 50 litres of milk and replaced it with the same quantity of water. He repeated the same process further two times. And thus milk in the container is only 'X - 122' litres. Then what is the quantity of milk in the final mixture?

  1. 122 litres

  2. 124 litres

  3. 128 litres

  4. 250 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The formula for the remaining amount of the original substance is X * (1 - r/X)^n. Here, 50 * (1 - 50/X)^3 = 122 is not the correct setup; rather, the amount of milk left is X * (1 - 50/X)^3 = X - 122. Solving for X gives 250. The final quantity of milk is 250 - 122 = 128.