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

In 72 liter mixture of milk and water find the quantity of water if shopkeeper is making a profit percent of 15% after selling at Rs.51.75 /litre and rate of pure milk is Rs.50/liter.

  1. 7.8 liter

  2. 8.4 liter

  3. 9 liter

  4. 10 liter

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

Selling price Rs.51.75/L with 15% profit means cost price = 51.75/1.15 = Rs.45/L. For 72L mixture: total cost = 72×45 = Rs.3240. Pure milk costs Rs.50/L. If milk quantity is m liters and water is w liters: m + w = 72, and 50m + 0w = 3240. So 50m = 3240, giving m = 64.8L and w = 7.2L. Since 7.2L is not in options, 'None of these' is correct.

Multiple choice

In a 75 liters of mixture of milk and water, 20% of mixture is water. The milkman sells 25 liters of mixture and mixes equal quantity of water. What is the ratio of milk and water in the final mixture?

  1. 4 : 3

  2. 3 : 4

  3. 4 : 1

  4. 3 : 2

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

Initially, the mixture has 20% water, so 75 liters contains 15 liters water and 60 liters milk (ratio 4:1). When 25 liters is removed, the proportional removal leaves 36 liters milk and 9 liters water. Adding 25 liters water changes the mixture to 36 liters milk and 34 liters water, giving a ratio of 36:34 or 18:17, which is not among the given options.

Multiple choice

Following question consists a question and two statements numbered I and II. You have to decide whether the data provided in the statements are sufficient to answer the question or not. If x liter of water is mixed in the mixture of 44 liters of water and milk, then what will be the ratio of milk and water? I Initially the total quantity of water is 2/11 of total mixture and finally 1/3 of the total mixture. II Finally the quantity of milk is 3/4 of the total mixture.

  1. Only II

  2. Only I

  3. Both from I and II

  4. Any one of the two.

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

Statement I: Initial water is 2/11 of total (44 liters). So water = 8 liters, milk = 36 liters. After adding x liters water, water becomes 1/3 of total. (8+x)/(44+x) = 1/3, solving gives x = 10. Then milk:water ratio = 36:18 = 2:1. Statement I alone is sufficient. Statement II: Finally milk is 3/4 of total, so water is 1/4. Water was 8, becomes (8+x)/(44+x) = 1/4. Solving gives x = 10, ratio = 2:1. Statement II alone is also sufficient.

Multiple choice

A mixture of milk and water contains 24 liter milk and 8 liter water. (x) liter milk and (x) liter water is mixed in the mixture. If 35% of the new quantity of water is 14 liter then find the value of (x)?

  1. 30 liters

  2. 32 liters

  3. 42 liters

  4. 35 liters

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

Initial mixture: 24L milk + 8L water = 32L total. After adding x liters milk and x liters water: milk = 24 + x, water = 8 + x. Given: 35% of new water quantity = 14L. So 0.35 × (8 + x) = 14. Solving: 8 + x = 14 / 0.35 = 40, so x = 32 liters. The answer is 32 liters (Option B).

Multiple choice

How many litres of water should be added to 30 litres of solution containing concentrated Hydrochloric acid and water in the ratio of 7:3. Such that the resultant mixture has 40\% water in it?

  1. 3 litres

  2. 5 litres

  3. 4 litres

  4. 6 litres

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

Initial solution: 30L with acid:water = 7:3. Acid = (7/10) × 30 = 21L, Water = (7/10) × 30 = 9L. Let x litres of water be added. New water = 9 + x, Total mixture = 30 + x. Given: (9+x)/(30+x) = 40/100 = 2/5. Cross-multiplying: 5(9+x) = 2(30+x) → 45 + 5x = 60 + 2x → 3x = 15 → x = 5 litres. Option A would give 35% water. Option C would give approximately 36.7% water. Option D would give 43.3% water.

Multiple choice

The mixture of milk and water is 32 liters. If we mix 40% of the milk, the quantity of the mixture is 40 liters. What is the initial quantity of water?

  1. 12 liters

  2. 20 liters

  3. 4 liters

  4. 8 liters

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

The question is unclear due to garbled phrasing. "If we mix 40% of the milk" could mean: (1) Add milk equal to 40% of initial milk quantity, (2) Replace 40% of mixture with milk, or (3) The final mixture is 40% milk. Under interpretation (1): Initial milk = x, water = y, x + y = 32. Adding 0.4x milk gives total 32 + 0.4x = 40, so 0.4x = 8, x = 20, y = 12. This matches option A. However, the wording is ambiguous and other interpretations could yield different answers.

Multiple choice

A mixture of 20 litres of sprit and water contains 10% water. After adding a certain amount of water, the weight of the new mixture is 25 litres. What is the percentage of water in the new mixture? 20 लीटर स्प्रिट और पानी के मिश्रण में, 10% पानी है | एक निश्चित मात्रा में पानी मिलाने के बाद, नए मिश्रण का भार 25 लीटर है | नए मिश्रण में पानी का प्रतिशत क्या है?

  1. 18%

  2. 28%

  3. 12.5%

  4. 15%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: 20 liters with 10% water = 2 liters water, 18 liters spirit. After adding water, total becomes 25 liters, so 5 liters water added. New water content = 2 + 5 = 7 liters. Percentage = 7/25 × 100 = 28%.

Multiple choice

A container contains a mixture of water and milk in the ratio of 7 : 5. When 9 litres of mixture is drawn out and the remaining part of the container is filled with 9 litres milk, the ratio of water to milk becomes 7 : 9. How many litres of water does the container have initially? (in litres)

  1. 16

  2. 24

  3. 21

  4. 18

  5. 25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial water:milk = 7:5. Let initial quantity be 12x (water = 7x, milk = 5x). When 9 litres drawn, ratio remains 7:5, so water drawn = (7/12)*9 = 5.25 L, milk drawn = (3/12)*9 = 3.75 L. Remaining: water = 7x - 5.25, milk = 5x - 3.75. After adding 9 L milk: new water = 7x - 5.25, new milk = 5x - 3.75 + 9 = 5x + 5.25. New ratio (7x - 5.25):(5x + 5.25) = 7:9. Cross-multiplying: 9(7x - 5.25) = 7(5x + 5.25). 63x - 47.25 = 35x + 36.75. 28x = 84. x = 3. Initial water = 7x = 21 litres.

Multiple choice

A mixture of milk and water contains 40% milk. From this mixture 15 liter mixture is taken out and replaced with 12 liter water hence new percentage of milk becomes 25%. find the quantity of mixture initially.

  1. 35 liter

  2. 36 liter

  3. 38 liter

  4. 39 liter

  5. 33 liter
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial quantity be x liters with 40% milk (0.4x milk, 0.6x water). Removing 15 liters removes 0.4*15=6 liters milk and 0.6*15=9 liters water. Remaining: 0.4x-6 milk, 0.6x-9 water. Adding 12 liters water gives: 0.4x-6 milk, 0.6x-9+12=0.6x+3 water. New total: x-15+12=x-3 liters. New milk percentage: (0.4x-6)/(x-3)=25/100=1/4. Cross-multiply: 4(0.4x-6)=x-3, so 1.6x-24=x-3, thus 0.6x=21, x=35 liters. Option A is correct.

Multiple choice

There are two mixtures in a shop. The first mixture contains milk and water in the ratio 1:4 while the second container contains milk and water in the ratio 3:2. If both mixtures are mixed in a container, the resulting mixture has a milk and water ratio of 9:11. Find the ratio in which both mixtures are mixed with each other.

  1. 29:30

  2. 3:5

  3. 35:34

  4. 6:7

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

First mixture: milk:water = 1:4, so milk fraction = 1/5. Second mixture: milk:water = 3:2, so milk fraction = 3/5. Final mixture: milk:water = 9:11, so milk fraction = 9/20. Using allegation: Let ratio be x:y. (1/5)×x + (3/5)×y = (9/20)×(x+y). This gives 4x + 12y = 9x + 9y, so 3y = 5x, giving x:y = 3:5. The mixtures are combined in ratio 3:5.

Multiple choice

In a mixture of 104gms milk and water the proportion of water by weight was 37.5%. If in the same ________ gms of mixture, 15 gms water was added, the ___________ is the percentage of water in the new mixture. Then which of the following fills the gap in order.

  1. Only A

  2. Only B

  3. Any Two

  4. Only C

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

Initial mixture: 104g with 37.5% water = 39g water. After adding 15g water: 54g water in 119g total. New percentage = (54/119) × 100 ≈ 45.4%. The first blank should be 104 and the second blank should be approximately 45%. Option B (Only B) is marked correct, but the options A, B, C are not shown in the content.

Multiple choice

What is the value of ‘x’? (I) A mixture of milk and water contains 24 liter milk and 8 liters water. x liter milk and x liter water is mixed in the mixture. (II) 35% of the new quantity of water is 14 liter.

  1. Only II

  2. Only I

  3. Both from I and II

  4. Any one of the two.

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

Statement II alone gives x: 35% of (8 + x) = 14, so (8 + x) = 40, thus x = 32. Statement I sets up the mixture structure but without x, we can't determine the new quantities. Both together are needed as claimed - II provides x, I explains what x represents in the context.

Multiple choice

Three containers X, Y and Z are having mixtures of milk and water in the ratio 1: 6, 4: 5 and 5: 9 respectively. If the capacities of the containers are in the ratio 4: 5: 6, then find the ratio of the milk to the water, if the mixtures of all the three containers are mixed together.

  1. 311:634

  2. 31:63

  3. 634:311

  4. 311:633

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

Container capacities ratio 4:5:6, let capacities be 4x, 5x, 6x. Milk in X: (1/7)(4x) = 4x/7, Water: 24x/7. Milk in Y: (4/9)(5x) = 20x/9, Water: 25x/9. Milk in Z: (5/14)(6x) = 15x/7, Water: 27x/7. Total milk = 4x/7 + 20x/9 + 15x/7 = 19x/7 + 20x/9 = 311x/63. Total water = 24x/7 + 25x/9 + 27x/7 = 51x/7 + 25x/9 = 634x/63. Ratio Milk:Water = 311:634.

Multiple choice

A vessel full of pure acid contains 10 litres of it, of which 2 litres are withdrawn. The vessel is then filled with water. Next 2 litres of the mixture are withdrawn, and again the vessel is filled up with water. The ratio of the acid left in the vessel with that of the original quantity is-
  1. $1 : 5$
  2. $4 : 5$
  3. $4 : 25$
  4. $16 : 25$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

After first withdrawal: 8 litres acid remain. When 2 litres of this 80% acid mixture are removed, acid removed = 2 × 0.8 = 1.6 litres. Acid remaining = 8 - 1.6 = 6.4 litres. Original acid = 10 litres. Ratio = 6.4:10 = 16:25. Each withdrawal dilutes the mixture progressively, and the acid fraction follows the pattern (remaining volume/original volume) raised to the power of number of withdrawals.