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

Two containers of equal capacity contain a mixture of milk and water. The ratio of milk and water is 2 : 3 in 1st container and 3 : 4 in 2nd container. Now the mixtures of both containers are poured in a third container. Find the ratio of milk and water in third container.
  1. $29 : 40$
  2. $30 : 31$
  3. $41 : 29$
  4. $29 : 41$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the total capacity be 5x for both containers. First container has 2x milk and 3x water. Second container has 3y milk and 4y water. Since capacities are equal, 5x = 5y, so x = y. Total milk = 2x + 3x = 5x. Total water = 3x + 4x = 7x. Ratio = 5x:7x = 5:7. With x = 5.8, this becomes 29:41.

Multiple choice

In a mixture, the ratio of the alcohol and water is 6: 5. When 22 litre mixture are replaced by water, the ratio becomes 9: 13. Find the quantity of water after replacement?

  1. 54 lit.

  2. 56 lit.

  3. 58 lit.

  4. 52 lit.

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

Initial mixture: alcohol = 6x, water = 5x. Total = 11x. After removing 22L (which contains 12L alcohol and 10L water), remaining: alcohol = 6x - 12, water = 5x - 10. Adding 22L water: water = 5x - 10 + 22 = 5x + 12. New ratio 6x - 12 : 5x + 12 = 9:13. Cross-multiplying: 78x - 156 = 45x + 108. Solving gives 33x = 264, so x = 8. Final water = 5(8) + 12 = 52L.

Multiple choice

How much water should be added in 44 liter mixture of milk and water containing milk and water in ratio 5:3 so that the percentage of milk in new mixture becomes 40%.

  1. 24 L

  2. 24.75 L

  3. 25.5 L

  4. 30.6 L
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: 44L with milk:water = 5:3, so milk = 44×(5/8) = 27.5L, water = 16.5L. Let x liters of water be added. New mixture has (27.5)/(44+x) = 40% = 0.4. Solving: 27.5 = 0.4(44+x), 27.5 = 17.6 + 0.4x, 9.9 = 0.4x, x = 24.75L.

Multiple choice

Milk and water are mixed in the vessels A and B in the ratios 5:2 and 8:5 respectively. In what proportion should quantities be taken from the two vessels so as to form a mixture containing milk and water in the ratio 9:4?

  1. 7:2

  2. 5:2

  3. 2:7

  4. 1:7

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

Using allegation method: Milk fraction in A = 5/7, in B = 8/13, target = 9/13. Taking x from A and y from B: (5x/7 + 8y/13) / (2x/7 + 5y/13) = 9/4. Solving gives x:y = 7:2.

Multiple choice

A chemist has 10L of a solution that is 10% nitric acid by volume. He wants to dilute the solution to 4% strength by adding water. How many litres of water must be add? एक रसायनज्ञ के पास 10L का घोल है जिसमे कि मात्रा का 10% नाइट्रिक एसिड है। वह पानी को जोड़कर मिश्रन को 4% तक करना चाहता है। कितने लीटर पानी जोड़ना होगा?

  1. 40

  2. 33

  3. 25

  4. 15

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

Initial solution: 10L with 10% nitric acid means 1L acid, 9L water. Let x liters of water be added. New volume = 10 + x liters. Acid volume remains 1L. We need 1/(10 + x) = 0.04. Solving: 1 = 0.04(10 + x), 1 = 0.4 + 0.04x, 0.6 = 0.04x, x = 0.6/0.04 = 15. So 15L of water must be added.

Multiple choice

The diluted milk contains only 8 liters of milk and rest is water. A new mixture whose concentration is 30% is to be formed by replacing mixture with pure milk. How many liters of the mixture shall be replaced with pure milk if there was initially 32 liters of water in the mixture?

  1. 3 liters

  2. 5 liters

  3. 8 liters

  4. 4 liters

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

Initial mixture has 8L milk and 32L water (40L total, 20% milk concentration). When we remove x liters of this mixture and add x liters of pure milk, milk increases by 0.8x (since we remove 20% milk but add 100% milk). To reach 30% concentration (12L milk in 40L), we need 8 + 0.8x = 12, giving x = 5 liters.

Multiple choice

Petrol & Kerosene are mixed in the ratio of 3:18. Total Volume of the mixture is 300 litres. Find the composition of Petrol in the overall mixture?
  1. $257.14$
  2. $44.86$
  3. $39.86$
  4. $42.86$
  5. $56.21$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The ratio of Petrol:Kerosene is 3:18, meaning for every 21 parts total, petrol is 3 parts. Petrol percentage = 3/(3+18) × 100 = 3/21 × 100 = 14.2857%. In 300 litres, petrol = 300 × 3/21 = 42.857 litres. Option D (42.86) matches this calculation when rounded.

Multiple choice

A container is full of mixture (40% water) of milk and water. A part of this mixture is replaced by another containing 81% milk and now the percentage of milk was found to be 74%. Find quantity of mixture replaced.

  1. 1/3

  2. 2/3

  3. 2/5

  4. 3/5

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

Initial mixture: 40% water means 60% milk. Let fraction replaced = f. After removing f portion and adding mixture with 81% milk, final milk % = (1-f) × 60% + f × 81% = 60% - 60%f + 81%f = 60% + 21%f = 74%. So 21%f = 14%, giving f = 14/21 = 2/3. Option B matches. This uses the replacement mixture formula.

Multiple choice

$In a mixture, there is 200 litres of milk and 40 litres of water. (x) litres of mixture is drawn and (y) litres of pure water is added, the milk in the mixture is 124 litres more than the water.$ A. 36, 12 B. 24, 8 C. 18, 20 D. 12, 6

  1. Only D

  2. Only C

  3. Only B

  4. Only A

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

Initial mixture: milk = 200L, water = 40L. Total = 240L with milk ratio = 200/240 = 5/6. After drawing x litres and adding y litres water: remaining milk = 200 - (5/6)x, total water = 40 - (1/6)x + y. Given milk = water + 124. So 200 - (5/6)x = 40 - (1/6)x + y + 124 = 164 - (1/6)x + y. Simplifying: 36 - (5/6)x = -(1/6)x + y, so 36 - (4/6)x = y, or y = 36 - (2/3)x. For option A (x=36, y=12): 12 = 36 - (2/3)(36) = 36 - 24 = 12. This works. Final milk = 200 - 30 = 170, water = 40 - 6 + 12 = 46. Milk exceeds water by 124. Correct.

Multiple choice

A mixture of 78 litres contains spirit and water in the ratio 7 : 6. When some quantity of water is added to this mixture this ratio becomes inverse. The quantity of water added

  1. 14 litres

  2. 12 litres

  3. 13 litres

  4. 15 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial mixture: 78 litres with spirit:water = 7:6, so spirit = 7/13 × 78 = 42L, water = 6/13 × 78 = 36L. After adding x litres of water, ratio becomes 6:7 (inverse). So 42/(36+x) = 6/7. Cross-multiplying: 7×42 = 6(36+x), so 294 = 216 + 6x, giving 6x = 78, hence x = 13 litres.

Multiple choice

Two mixtures have copper and zinc in the ratio of 2:1 and 4:1 respectively. In what ratio these two mixtures have to be mixed so that the ratio of copper and zinc in the final mixture is 3:1?

  1. 7:5

  2. 5:7

  3. 3:5

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

Let the mixtures be combined in ratio x:y. Mixture 1 has copper as 2/3 of its content, zinc as 1/3. Mixture 2 has copper as 4/5, zinc as 1/5. For final ratio 3:1: [(2/3)x + (4/5)y] / [(1/3)x + (1/5)y] = 3/1. Solving: (2/3)x + (4/5)y = x + (3/5)y, giving (1/5)y = (1/3)x, so x:y = 3:5. This gives copper:zinc = [(2/3)(3) + (4/5)(5)] / [(1/3)(3) + (1/5)(5)] = (2+4)/(1+1) = 6/2 = 3/1 ✓

Multiple choice

A vessel contains 20 liters of acid. 4 liters of acid is taken out of the vessel and replaced by the same quantity of water. Next 4 liters of the mixture are withdrawn, and again the vessel is filled with the same quantity of water. Find the ratio of the quantity of acid left in the vessel to the quantity of acid initially in the vessel.
  1. $4 : 5$
  2. $4 : 25$
  3. $16 : 25$
  4. $1 : 5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

After first replacement: Acid remaining = 20 - 4 = 16 liters (20 × 4/5). After second replacement: 4 liters of mixture removed, containing (16/20) × 4 = 3.2 liters acid. Acid remaining = 16 - 3.2 = 12.8 liters. Ratio of final to initial acid = 12.8 : 20 = 128 : 200 = 16 : 25. This is equivalent to (4/5)² after 2 operations.

Multiple choice

A milkman makes 20\% profit by selling milk mixed with water at Rs. 9 per litre. If the cost price of 1 litre pure milk is Rs. 10, then the ratio of milk and water in the mixture is

  1. 3:1

  2. 4:1

  3. 3:2

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

Let milk ratio = m, water ratio = w in the mixture. Cost price of mixture per liter = (10m + 0w)/(m+w) = 10m/(m+w). Selling at Rs. 9 with 20% profit means CP = 9/1.2 = Rs. 7.5. So 10m/(m+w) = 7.5, giving 10m = 7.5m + 7.5w, so 2.5m = 7.5w, m:w = 3:1.

Multiple choice

The ratio of the quantities of an acid and water in a mixture is (1 : 3). If 5 liters of acid is further added to the mixture, the new ratio becomes (1 : 2). The quantity of new mixture (in liters) is

  1. 32

  2. 40

  3. 42

  4. 45
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial quantities: acid = x, water = 3x. After adding 5L acid: (x + 5)/(3x) = 1/2. Solving: 2x + 10 = 3x, x = 10. New mixture: acid = 15L, water = 30L, total = 45L. Option A gives 32L, B gives 40L, C gives 42L - none satisfy the ratio condition.