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

Directions : Select the correct alternative from the given choices. There is a 40 litre solution of milk and water with concentration of milk as 30%. Initially, 10 litres of the solution is replaced with 10 litres of water. After some time, 10 litres of the new solution is replaced with 10 litres of milk. What is the concentration of milk in the solution now?

  1. 58.125%

  2. 41.875%

  3. 35.625%

  4. 64.375%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: 40L, 30% milk = 12L milk, 28L water. Replace 10L solution with 10L water: 10L of solution contains 3L milk, 7L water. Remaining: 9L milk, 21L water + 10L water = 9L milk, 31L water. Replace 10L of new solution (which is 9/40 milk = 22.5% milk) with 10L milk: 10L of new solution has 2.25L milk. Remaining milk = 9 - 2.25 = 6.75L. Add 10L milk: 6.75 + 10 = 16.75L milk. Concentration = 16.75 / 40 = 41.875%.

Multiple choice

If 160 litres of a solution of milk and water has 25% water, then how much water should be added to the solution so that the percentage of milk becomes 60%?

  1. 20 litres

  2. 30 litres

  3. 35 litres

  4. 40 litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial solution: 160 liters, 25% water (40L), 75% milk (120L). We add x liters of water. New total = 160 + x. Milk remains 120L. We want milk to be 60% of the new total: 120 / (160 + x) = 0.6. 120 = 0.6 * (160 + x) = 96 + 0.6x. 24 = 0.6x. x = 24 / 0.6 = 40 liters.

Multiple choice

Two containers A and B contain alcohol and water in the ratio 4 : 3 and 2 : 3, respectively. If mixtures from both the containers are mixed to obtain a new mixture having half alcohol and half water, find the ratio in which these are mixed.

  1. 4 : 3

  2. 5 : 4

  3. 6 : 5

  4. 7 : 5

  5. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using alligation: Container A has 4/7 alcohol, Container B has 2/5 alcohol. Target is 1/2. |2/5 - 1/2| = 1/10. |4/7 - 1/2| = 1/14. Ratio = (1/10) : (1/14) = 14 : 10 = 7 : 5.

Multiple choice

In a 140 litres of mixture of milk and water, percentage of water is only 30%. The milkman gave 20 litres of this mixture to a customer. Then he added equal quantities of pure milk and water to the remaining mixture. As a result the respective ratio of milk and water in the mixture became 2 : 1. What was the quantity of milk added? (in litres)

  1. 12

  2. 16

  3. 18

  4. 8

  5. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial: 140L, 30% water (42L), 70% milk (98L). Remove 20L: 140-20=120L remaining. Ratio 7:3 remains, so 84L milk, 36L water. Add x L of each: (84+x)/(36+x) = 2/1. 84+x = 72+2x => x = 12.

Multiple choice

A jar was full with honey. A person to drawn out 20% of the honey from the jar and replaced it with sugar solution. He done the same process 4 times and thus there was only 512 gm of honey left in the jar, the rest part of the jar was filled with the sugar solution. The initial amount of honey in the jar was:

  1. 1.25 kg

  2. 1 kg

  3. 1.5 kg

  4. 2.4 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for the remaining amount of honey is A = P(1 - r/100)^n. Here, 512 = P(1 - 20/100)^4, which is 512 = P(0.8)^4. 512 = P(0.4096), so P = 512 / 0.4096 = 1250 grams, which is 1.25 kg.

Multiple choice

There are two mixtures i.e. P and Q of spirit and water. The mixture P contains ratio of spirit to water as 5 : 8 and Q contains ratio of water to spirit as 4 : 5. 26 litres of mixture P and some quantity of Q is taken out and these two quantities are mixed together to form a new mixture. Ratio of spirit to water in this new mixture is 4 : 5. Find the quantity which was taken out from Q.

  1. 14

  2. 8

  3. 12

  4. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mixture P: Spirit/Water = 5:8. In 26L, Spirit = 10L, Water = 16L. Mixture Q: Water/Spirit = 4:5, so Spirit/Water = 5:4. Let x be the quantity of Q. Spirit = 10 + (5/9)x, Water = 16 + (4/9)x. Ratio (10 + 5/9x) / (16 + 4/9x) = 4/5. Cross-multiplying: 50 + 25/9x = 64 + 16/9x. 9/9x = 14, so x = 14.

Multiple choice

A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and same quantity of B is poured into can , the ratio of A and B becomes 7 : 9 ,litres of liquid A contained by the can initially was

  1. 7

  2. 10

  3. 17

  4. 21
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the initial quantities of liquids A and B be 7x and 5x. When 9 litres of the mixture are removed and replaced with 9 litres of B, the new ratio of A to B becomes (7x - 9 * 7/12) / (5x - 9 * 5/12 + 9) = 7/9, which simplifies to x = 3. Thus, the initial quantity of liquid A was 7 * 3 = 21 litres.

Multiple choice

A container has 30 litres of water. 3 litres of the mixture is taken out and replaced with 3 litres of spirit. If this process is carried out twice in total, what will be the quantity of water left in the final mixture?

  1. 24 litres

  2. 23 litres

  3. 24.3 litres

  4. 23.3 litres

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

Using the formula for replacement: Final amount = Initial * (1 - removed/total)^n. Here, 30 * (1 - 3/30)^2 = 30 * (0.9)^2 = 30 * 0.81 = 24.3 litres.

Multiple choice

Three glasses contain equal volumes of liquid mixtures of milk and water. The ratio of milk to water in the three glasses is 2 : 3, 4 : 1 and 3 : 2, respectively. The contents of the three glasses are mixed together in a jar. What is the ratio of milk to water in the final mixture in the jar?

  1. 3 : 4

  2. 5 : 4

  3. 3 : 2

  4. 4 : 5

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

Milk fractions are 2/5, 4/5, and 3/5. Water fractions are 3/5, 1/5, and 2/5. Summing these: Milk = (2+4+3)/5 = 9/5; Water = (3+1+2)/5 = 6/5. The ratio is 9:6, which simplifies to 3:2.