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

If 2 kg of metal, of which (\frac{1}{3}) is zinc and the rest is copper be mixed with 3 kg of metal of which (\frac{1}{4}) is zinc and the rest is copper, if both are mixed then what is the ratio of zinc to copper in the mixture?
  1. $2:3$
  2. $3:2$
  3. $43:17$
  4. $17:43$
  5. $15:17$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First metal: 2 kg with (1/3) zinc = 2/3 kg zinc, (2/3) copper = 4/3 kg copper. Second metal: 3 kg with (1/4) zinc = 3/4 kg zinc, (3/4) copper = 9/4 kg copper. Total zinc = 2/3 + 3/4 = 17/12 kg. Total copper = 4/3 + 9/4 = 43/12 kg. Ratio zinc:copper = (17/12):(43/12) = 17:43.

Multiple choice

A container has 30 L of water. If 3 L of water is replaced by 3 L of spirit and this operation is repeated twice , what will be the quantity of water in the new mixture?

  1. 27.1

  2. 25.5

  3. 14.4

  4. 24.3

  5. 22
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial: 30L water (0% spirit). After first replacement: 3L water removed, 3L spirit added → 27L water + 3L spirit. Water concentration = 27/30 = 0.9. Second operation: 3L of mixture removed containing 0.9 × 3 = 2.7L water and 0.3L spirit. Remaining: 27 - 2.7 = 24.3L water, 3 - 0.3 = 2.7L spirit. Add 3L spirit: Final = 24.3L water + 5.7L spirit = 30L total. Water quantity = 24.3L. Formula: Final water = 30 × (1 - 3/30)² = 30 × (0.9)² = 30 × 0.81 = 24.3L.

Multiple choice

Two equal glasses are respectively (\frac{1}{4})th and (\frac{3}{5})th full of milk. They are then filled up with water and the contents are mixed in another glass. Find the ratio of milk and water in another glass.
  1. $13: 17$
  2. $15: 19$
  3. $17: 23$
  4. $18: 25$

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

Glass 1 has 1/4 milk, 3/4 water when filled. Glass 2 has 3/5 milk, 2/5 water when filled. Combined milk = 1/4 + 3/5 = 17/20. Combined water = 3/4 + 2/5 = 23/20. Ratio milk:water = 17:23.

Multiple choice

A mixture contains milk and water in the ratio 5 : 3. If 20 litres of water is added to the mixture, the ratio of milk and water becomes 3 : 2. Find the quantity of milk in the original mixture.

  1. 320

  2. 280

  3. 300

  4. 250

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

Let milk = 5x, water = 3x. After adding 20L water: 5x/(3x+20) = 3/2. Cross-multiply: 10x = 9x + 60, so x = 60. Milk = 5x = 300L. Option C is correct. Option A (320) would come from incorrect algebra. Option B (280) and D (250) don't satisfy the ratio condition.

Multiple choice

Two varieties of rice are mixed in the ratio 2: 3. The price of the mixture is Rs 12 per kg and the price of the variety having lower weight is Rs 10 per kg. Find the price of the other variety.

  1. Rs 12

  2. Rs 12.5

  3. Rs 13

  4. Rs 13.33

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

Using allegation: Two rice varieties mixed in ratio 2:3. Let price of second variety be x. Using weighted average: (2×10 + 3×x)/(2+3) = 12. Solving: 20 + 3x = 60, so 3x = 40, x = 40/3 ≈ 13.33. Option D (Rs 13.33) is correct. Option A equals the mixture price, not the individual variety price. Options B and C are incorrect calculations.

Multiple choice

The concentration of three milk solutions A, B and C are 10%, 20% and 30% respectively. They are mixed in the ratio 2: 3: N resulting in a 23% concentration solution. Find N.

  1. 7

  2. 6

  3. 5

  4. 4

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

Using allegation: 10%, 20%, and 30% solutions mixed in ratio 2:3:N to get 23%. Setup: (2×10 + 3×20 + N×30)/(2+3+N) = 23. Solving: (20 + 60 + 30N)/(5+N) = 23, so 80 + 30N = 115 + 23N, giving 7N = 35, N = 5. Option C is correct. Options A, B, and D don't satisfy the equation.

Multiple choice

Two vessels contain milk and water in the ratio 3:5 and 6:1. Find the ratio in which the contents of the two vessels have to be mixed to get a new mixture in which the ratio of milk and water is 7:3.

  1. 91: 44

  2. 17: 81

  3. 44: 91

  4. 81: 17

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

Using allegation: Vessel 1 has 3/8 = 0.375 milk, Vessel 2 has 6/7 ≈ 0.857 milk. Target is 7/10 = 0.7. The ratio is (0.857 - 0.7) : (0.7 - 0.375) = 0.157 : 0.325 = 44 : 91. So mix in ratio 44:91.

Multiple choice

Namish stole wine from a cask of Sangram which contained 35% spirit and he replaced what he had stolen by wine containing only 20% spirit. The butt was then 25% strong only. How much of the butt did he steal?

  1. 1/3

  2. 2/3

  3. 3/4

  4. 1/4

  5. 1/2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the fraction stolen. The original butt has 35% spirit. After stealing x portion, (1-x) remains at 35% spirit. This is mixed with x portion at 20% spirit to get 25% strength. Equation: (1-x)(35%) + x(20%) = 25%. Simplifying: 35 - 35x + 20x = 25, so 35 - 15x = 25, giving 15x = 10 and x = 2/3. This is a standard alligation problem.

Multiple choice

There are three vessels of 10 liters in which the ratio of milk and water is 2 : 1, 3 : 1, and 3 : 2 respectively. If all three utensils are put in a large vessel, find the ratio of milk and water in the new mixture?
  1. $118 : 53$
  2. $121 : 59$
  3. $122 : 53$
  4. $121 : 53$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For each vessel, calculate actual milk and water quantities separately using ratio parts, then sum across vessels. Vessel 1 (2:1): Milk=20/3 L, Water=10/3 L. Vessel 2 (3:1): Milk=15/2 L, Water=5/2 L. Vessel 3 (3:2): Milk=6 L, Water=4 L. Total Milk=121/6 L, Total Water=59/6 L. Ratio = (121/6):(59/6) = 121:59 after cancelling the common denominator.

Multiple choice

A mixture of 70 liters of milk and water contains 20% milk. What quantity of water should be added to the mixture to increase the percentage of water by 25% in the new mixture?

  1. 20 liters

  2. 14 liters

  3. 18 liters

  4. 16.8 liters
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

70L mixture has 20% milk = 14L milk, 56L water (80% water). Adding x liters water gives (56+x)L water in (70+x)L total. New water percentage = (56+x)/(70+x). We want 25% increase from 80%, so new percentage = 100% (since 80×1.25=100). So (56+x)/(70+x)=1, giving x=14L.

Multiple choice

A container contains 50 litres of milk. From this container 5 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

  1. 28.50

  2. 36.45

  3. 25.5

  4. 32.25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a dilution problem. After each replacement, milk reduces by factor (45/50)=0.9. After 3 replacements: 50×(0.9)³ = 50×0.729 = 36.45 litres. Alternatively: 50×(45/50)³ = 50×(9/10)³ = 50×729/1000 = 36.45.

Multiple choice

In a 24 litre milk water solution, where concentration of milk is 250/3%. What amount of water should be added in to the solution so that concentration of milk becomes 50%?

  1. 16 litre

  2. 20 litre

  3. 24 litre

  4. 8 litre
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is impossible as stated. A 24L solution cannot have milk concentration of 250/3% ≈ 83.33% because that would require 20L of milk, but then the concentration would be (20/24)×100 = 83.33%, not 250/3% = 83.33%. The 250/3% notation is garbled. If milk is 20L in 24L solution, to get to 50% concentration by adding water: 20/(24+x) = 0.5, so x = 16L. Answer A matches this.

Multiple choice

A trader mixes two types of tea varieties with a cost of Rs 43 and Rs 52 . If he sells the mixture of Rs 54 at 12.5 % profit, then in what ratio he mixes two types of tea varieties ?

  1. 4 : 5

  2. 5 : 3

  3. 3 : 4

  4. 5 : 6

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

The cost price of the mixture is 54 / 1.125 = Rs 48. Using alligation: difference between Rs 52 and Rs 48 is 4, difference between Rs 48 and Rs 43 is 5. Therefore, the ratio is 4:5 (Tea costing Rs 52 : Tea costing Rs 43).

Multiple choice

3 containers having capacities in the ratio 2: 3: 1 contain mixture of liquids A and B such that the ratio of A to B in them is 2: 3, 1: 4 and 3: 7 respectively. If all the three containers are emptied in a single container, what will be the ratio of A to B in the final mixture?
  1. $12: 23$
  2. $23: 12$
  3. $17: 43$
  4. $43: 17$

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

Let capacities be 2x, 3x, x. Container 1 (capacity 2x) has A:B = 2:3, so A = (2/5)×2x = 4x/5, B = 6x/5. Container 2 (capacity 3x) has A:B = 1:4, so A = (1/5)×3x = 3x/5, B = 12x/5. Container 3 (capacity x) has A:B = 3:7, so A = (3/10)×x = 3x/10, B = 7x/10. Total A = 4x/5 + 3x/5 + 3x/10 = 17x/10. Total B = 6x/5 + 12x/5 + 7x/10 = 43x/10. Ratio A:B = 17:43.