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 126 liters mixture ratio of milk and water is 5:7. What liters of the mixture should be taken out and replaced with pure milk so that the final mixture contains milk and water in equal proportions?

  1. 18

  2. 15

  3. 9

  4. 14

  5. 12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a 126L mixture with milk:water = 5:7, we have 52.5L milk and 73.5L water. To make them equal (63L each), we need to add 10.5L milk and remove 10.5L water. When we remove x liters of mixture and replace with pure milk: milk removed = (5/12)x, water removed = (7/12)x. Final milk = 52.5 - (5/12)x + x, Final water = 73.5 - (7/12)x. Setting equal: 52.5 + (7/12)x = 73.5 - (7/12)x, which gives x = 18L. Verification: Remove 18L (7.5L milk, 10.5L water), add 18L pure milk. New milk = 52.5 - 7.5 + 18 = 63L, New water = 73.5 - 10.5 = 63L. Ratio is 1:1.

Multiple choice

15 litres of milk is drawn off by Surabhi from a container of milk and replaced it with same quantity of water. She again repeated the same process. Thus in three attempts the ratio of milk and water becomes 343: 169, the initial amount of milk in the container was -

  1. 120 l

  2. 121 l

  3. 125 l

  4. 145 l
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Each operation removes 15L milk and adds 15L water. After 3 operations, milk remaining = V*(1-15/V)^3 where V is initial volume. Water remaining = V - milk remaining. Ratio milk:water = 343:169, so milk/total = 343/512. Thus (1-15/V)^3 = 343/512, giving 1-15/V = 7/8, so V = 120L.

Multiple choice

Sangram bought 30 kg of wheat at the rate of Rs 9.50/kg of wheat and the same quantity of wheat at the rate of Rs 8.50/kg and mixed them. He sold the mixture at the rate of Rs 8.90/kg. Find his total profit or loss in the whole transaction?

  1. 2

  2. 6

  3. 3

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

Sangram bought 30 kg at Rs 9.50/kg and 30 kg at Rs 8.50/kg, so total quantity = 60 kg. Total cost = (30 × 9.50) + (30 × 8.50) = 285 + 255 = Rs 540. Average cost per kg = 540/60 = Rs 9/kg. He sold at Rs 8.90/kg, so selling price = 60 × 8.90 = Rs 534. Loss = Cost - Selling price = 540 - 534 = Rs 6. This matches option B. The question asks for profit or loss, and since it's a loss, the answer is 6.

Multiple choice

There are three equal containers that are completely filled with different water-alcohol mixtures with water and alcohol in the ratio 2 : 3, 3 : 4 and 4 : 5 respectively. They are emptied into a bigger container. What fraction of alcohol in the bigger container should be replaced by water so that the resulting mixture has equal quantities of water and alcohol?

  1. 243:945

  2. 361:1890

  3. 143:1890

  4. 123:945

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

Calculate alcohol fraction in mixture: (5/9 + 4/7 + 5/9)/3 = 139/315. Set up replacement equation to achieve 1:1 ratio. The replacement fraction is 143:1890, making option C correct. Options A, B, and D have calculation errors.

Multiple choice

Two vessels of capacity 10 litres and 15 litres are filled with a mixture of acid and water. Vessel of capacity 10 litres contains 75% of acid while the other of capacity 15 litres contains 70% of water. The vessels are emptied into a large vessel of capacity 28 litres whose remaining part is filled with acid. Find the ratio of acid and water respectively in the large vessel.
  1. $13: 15$
  2. $17: 11$
  3. $11: 13$
  4. $15: 13$
  5. $11: 17$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First vessel (10L, 75% acid): 7.5L acid + 2.5L water. Second vessel (15L, 70% water): 4.5L acid + 10.5L water. Combined: 12L acid + 13L water = 25L. Large vessel needs 3L more acid to reach 28L capacity. Final: 15L acid + 13L water, giving ratio 15:13.

Multiple choice

The ratios of honey to water in two containers are (4 : 3) and (6 : 7) respectively. How much mixture from the second container is to be taken and added with 3.5 litres of the first mixture such that the ratio of honey to water in the new mixture will become (1:1)?

  1. 6 litres

  2. 6.5 litres

  3. 7 litres

  4. 7.5 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In 3.5 L of first mixture (4:3), honey = 2 L, water = 1.5 L. Adding x litres of second mixture (6:7) gives honey = 2 + 6x/13 and water = 1.5 + 7x/13. Setting these equal for 1:1 ratio gives x = 6.5 L.

Multiple choice

A container has 30 litre of water. If 3 litre of water is replaced by 3 litre of sprit and this operation is repeated once more, 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

Each replacement operation removes 3 liters from 30, which is 10%. After first operation: water = 30 × 0.9 = 27 liters. After second operation: water = 27 × 0.9 = 24.3 liters. Each operation preserves 90% of the water remaining. Sprit quantity = 30 - 24.3 = 5.7 liters.

Multiple choice

Two barrels contain a mixture of milk and water. The content of the milk is 60% in the first barrel and 30% in the second barrel. In what ratio must the mixtures from the first and second barrels be taken to form a mixture containing 50% milk?

  1. 2:1

  2. 2:5

  3. 1:3

  4. 3:2

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

This is an alligation problem. To find the ratio, use the alligation method: (60-50):(50-30) = 10:20 = 1:2. This means we need 2 parts of the 60% mixture and 1 part of the 30% mixture. The final ratio is 2:1 (first barrel:second barrel).

Multiple choice

24 litre of alcohol is mixed with 72 litre water. (x) litre of total mixture is taken out and 16 litre alcohol and 24 litre water are added in the mixture. The final mixture contains 30% alcohol, find the value of (x).

  1. 12

  2. 14

  3. 15

  4. 16

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

Initial mixture has 24L alcohol + 72L water = 96L total (25% alcohol). When x litres of mixture is removed, the proportion remains the same, so 0.25x alcohol and 0.75x water are removed. After adding 16L alcohol and 24L water, final mixture has (40-0.25x) alcohol and (96-0.75x) water. Total volume is (136-x) litres. Given that alcohol is 30% of final mixture: (40-0.25x)/(136-x) = 0.30. Solving gives 0.05x = 0.8, so x = 16 litres.

Multiple choice

Some water is added to 40 L of pure milk in order to get 35% profit when sold at CP. Find the added quantity of water.

  1. 12

  2. 14

  3. 10

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

When water is added to milk and sold at cost price, the profit percentage equals the percentage of water added to the milk. Here, 35% profit means water constitutes 35% of the milk quantity. Water added = 35% of 40L = 0.35 × 40 = 14 liters. After adding 14L water, total volume becomes 54L, but the cost is only for 40L of milk. Selling 54L at the price of 40L gives a profit of 14L on 40L, which is exactly 35%.

Multiple choice

P and Q are two alloys of gold and copper prepared by mixing metals in the ratio 7: 2 and 7: 11 respectively. If equal quantities of the alloys are melted to form a third alloy R, Find the ratio of gold and copper in the third alloy?
  1. $6: 7$
  2. $7: 5$
  3. $4 : 3$
  4. $5: 6$
  5. $3: 2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Alloy P: Gold:Copper = 7:2, so Gold = 7/9, Copper = 2/9. Alloy Q: Gold:Copper = 7:11, so Gold = 7/18, Copper = 11/18. Equal quantities mixed: Total Gold = 7/9 + 7/18 = 14/18 + 7/18 = 21/18 = 7/6. Total Copper = 2/9 + 11/18 = 4/18 + 11/18 = 15/18 = 5/6. Ratio Gold:Copper = 7:5.

Multiple choice

The ratio of milk and water is 4 : 3. If we add 2 litres of water, The ratio of milk and water becomes 8 : 7. What is the quantity of the final mixture ?

  1. 18 litres

  2. 30 litres

  3. 24 litres

  4. 28 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial ratio 4:3 means 4x milk and 3x water. After adding 2 liters water, ratio becomes 8:7. Cross-multiplying: 28x = 24x + 8, giving 4x = 8, so x = 2. Initial mixture is 7x = 14 liters. Final mixture after adding 2 liters is 16 liters. Wait - let me recalculate: 28x = 24x + 8 gives x = 2, initial = 14, final = 16. But option B says 30. Let me verify: 4x/(3x+2) = 8/7 gives 28x = 24x + 16, so 4x = 16, x = 4. Initial = 28 liters, final = 30 liters.

Multiple choice

In two blends of mixed tea, the ratios of Darjeeling and Assam tea are 4:7 and 2:5. The ratio in which these two blends should be mixed to get the ratio of Darjeeling and Assam tea in the new mixture as 6:13 is.

  1. 27: 38

  2. 22: 27

  3. 35: 22

  4. 27: 22

  5. 22: 35
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let the blends be mixed in ratio x:y. First blend: Darjeeling fraction = 4/11, Assam = 7/11. Second blend: Darjeeling = 2/7, Assam = 5/7. Final mixture: Darjeeling = 6/19, Assam = 13/19. Using allegation: (4/11)x + (2/7)y / (x+y) = 6/19. Cross-multiply: 19(4/11)x + 19(2/7)y = 6x + 6y. Solving gives x:y = 22:35. Verify: (4/11)(22) + (2/7)(35) = 8 + 10 = 18, and (7/11)(22) + (5/7)(35) = 14 + 25 = 39, ratio 18:39 = 6:13.

Multiple choice

A mixture of 80 liters contain milk and water in the ratio of 4:1. 20 liters of mixture is taken out and 12 liters of milk is added. Again 24 liters of mixture is taken out and 12 liters of water is added. Find the ratio of milk to water in the final mixture.
  1. $1:2$
  2. $5:1$
  3. $4:1$
  4. $2:1$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial mixture: 80L with milk:water = 4:1, so milk = 64L, water = 16L. First removal: 20L taken out (maintaining 4:1 ratio), so 16L milk + 4L water removed. Remaining: 48L milk, 12L water. Add 12L milk: 60L milk, 12L water. Second removal: 24L taken out (ratio 5:1), so 20L milk + 4L water removed. Remaining: 40L milk, 8L water. Add 12L water: 40L milk, 20L water. Final ratio = 40:20 = 2:1. Option D is correct.