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

A container contains 330 litres of milk. Some quantity of milk is taken out and half of that quantity of milk, water is added in the container. Now ratio of milk to water in the container becomes 5:3. What is the quantity of water added in it?

  1. 80

  2. 90

  3. 120

  4. 60

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

Let x be the quantity of milk removed. Water added = x/2. Remaining milk = 330 - x. Final ratio (milk:water) = (330 - x) / (x/2) = 5/3. Cross-multiplying: 3(330 - x) = 5(x/2), so 990 - 3x = 2.5x, giving 990 = 5.5x, therefore x = 180. Water added = x/2 = 90 litres. Option A (80) is incorrect. Option C (120) would require x = 240, which is too much. Option D (60) would require x = 120.

Multiple choice

A Mixture of milk and water in a vessel has milk and water in the ratio 3: 1. 64 liters of mixture is taken out and replaced completely with milk such that the ratio of milk and water now becomes 4: 1. What will be the quantity of water left in the mixture if 20 liters of mixture is again taken out from the vessel?

  1. 30

  2. 40

  3. 120

  4. 60

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

Let total volume = T. Initial milk:water = 3:1, so milk = 3T/4, water = T/4. Removing 64L removes 48L milk and 16L water. Adding 64L milk gives milk = 3T/4 + 16, water = T/4 - 16. New ratio (3T/4 + 16)/(T/4 - 16) = 4/1. Solving: T = 320L. Water after first operation = 320/4 - 16 = 64L. After removing 20L (which contains 20 * 1/5 = 4L water), remaining water = 64 - 4 = 60L.

Multiple choice

The two pots have a mixture of milk and water. Milk in the first vessel is 90% and milk in the second vessel is 40%. In what proportion should the misture of both the utensils be mixed so that the mixture contains 70% milk?

  1. 2: 3

  2. 3: 2

  3. 4: 5

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

Using alligation rule: We need to mix 90% milk and 40% milk to get 70% milk. Differences from mean: 90 - 70 = 20 and 70 - 40 = 30. The ratio of quantities is the inverse of these differences, i.e., 3:2. This means 3 parts of 40% milk should be mixed with 2 parts of 90% milk to get 70% milk mixture.

Multiple choice

The two types of pulses were mixed in 2: 1 and a 10% profit was made by selling the mixture at ₹ 14 .30 per kilogram if the price per kilogram of the first pulse was ₹ 3 less than the second pulse. What is the price per kilogram?

  1. ₹13

  2. ₹17

  3. ₹18

  4. ₹15

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

Let the price of second pulse be Rs x/kg. Then first pulse costs Rs (x-3)/kg. Mixed in 2:1 ratio, average cost = [2(x-3) + 1(x)]/3 = (2x-6+x)/3 = (3x-6)/3 = (x-2) Rs/kg. Selling at Rs 14.30 with 10% profit means cost × 1.10 = 14.30, so cost = 14.30/1.10 = Rs 13/kg. Equating: x-2 = 13, so x = 15 (price of second pulse). First pulse costs 15-3 = Rs 12/kg. The question asks for price per kg - Rs 15 is the second pulse price shown in the answer.

Multiple choice

In a mixture of water and spirit, water is 40%. When 25 liter water is added in the mixture ratio of water and spirit becomes 3:2. Find the initial quantity of water in the mixture.

  1. 24 liters

  2. 36 liters

  3. 15 liters

  4. 20 liters

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

Let initial mixture = 100L (water = 40L, spirit = 60L). After adding 25L water: water = 65L, spirit = 60L. New ratio 65:60 = 13:12, not 3:2. Try initial water = W: W/(W+60) = 40/100 gives W = 40. After adding 25L: (40+25)/(60) = 65/60 = 13:12. Need W+25 = 1.5 × spirit. If spirit = S, W = 0.67S. Then (0.67S + 25)/S = 3/2. S = 50, so W = 20L. Answer D is correct.

Multiple choice

In a certain mixture of two liquids A and B; the B concentration of the mixture is 20%. When 20 liter of the mixture is removed and then 9 liter of a mixture of A and B having 55% A concentration is added the B concentration of the resultant mixture becomes 35%. Find the difference in the quantity of the liquid A in the initial and the final mixture.

  1. 9.75

  2. 11.05

  3. 20.80

  4. 10

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

Let initial mixture be 100L (20L B, 80L A). After removing 20L: remaining is 64L A, 16L B. Adding 9L of 55% A means 4.95L A, 4.05L B added. Final mixture: 68.95L A, 20.05L B in 89L total. Difference in A = 68.95 - 64 = 4.95L. In 100L equivalent: (4.95/89) × 100 ≈ 11.05L. This matches option B.

Multiple choice

The diluted alcohol contains only 7 litres of alcohol and the rest is water. A new mixture whose concentration is 40%, is to be formed by replacing alcohol. How many litres of mixture shall be replaced with pure alcohol if there was initially 28 litres of water in the mixture?
  1. $\(\frac{42}{5}\)$
  2. $\(\frac{35}{4}\)$
  3. $\(\frac{47}{8}\)$
  4. $\(\frac{14}{3}\)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original mixture: 7L alcohol + 28L water = 35L total (20% alcohol). Let x litres be replaced. Removed: 0.2x alcohol, 0.8x water. Added: x alcohol. Final alcohol = 7 - 0.2x + x = 7 + 0.8x. For 40% concentration: (7 + 0.8x)/35 = 0.4, giving x = 35/4 = 8.75 litres. The replacement maintains total volume while changing composition.

Multiple choice

Ratio of milk and water in mixture A and mixture B is 3:2 and 5:4 respectively. Mixture A and mixture B are mixed to form mixture C. If quantity of milk is 95 liters more than quantity of water in mixture C and the ratio of total quantity of mixture A to that of mixture B is 14: 9, then find total quantity of water in mixture C.

  1. 180L

  2. 360L

  3. 240L

  4. 380L

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

Let mixture A have quantity 14k and mixture B have quantity 9k (ratio 14:9). In mixture A (milk:water = 3:2), milk = 3/5 × 14k = 8.4k, water = 2/5 × 14k = 5.6k. In mixture B (milk:water = 5:4), milk = 5/9 × 9k = 5k, water = 4/9 × 9k = 4k. In mixture C: total milk = 8.4k + 5k = 13.4k, total water = 5.6k + 4k = 9.6k. Given: milk - water = 95 liters. So: 13.4k - 9.6k = 95, giving 3.8k = 95, so k = 25. Water in mixture C = 9.6k = 9.6 × 25 = 240 liters. Option C is correct.

Multiple choice

A dishonest milkman mixes milk to mineral water in the ratio of 5: 3. He sells the mixture at the cost price of milk and earns a profit of 20%. If the price of mineral water is Rs. 20 per litre, then the price of one litre milk is how much percentage more than that of one litre mineral water?

  1. 50%

  2. 60%

  3. 75%

  4. 80%

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

Let milk price be M and water price be W = Rs. 20/litre. Mixture ratio is 5:3. For every 8 litres of mixture, 5 litres are milk (cost 5M) and 3 litres are water (cost 3W = 60). Cost price of 8 litres = 5M + 60. Selling price of 8 litres = 8M (selling at milk price). Profit = 20%, so 8M = 1.2 × (5M + 60). Solving: 8M = 6M + 72, so 2M = 72, M = 36. Water price = 20. Difference = 36 - 20 = 16. Percentage more = (16/20) × 100 = 80%.

Multiple choice

In a mixture of 170 liters of milk and water, the ratio of milk and water is 12: 5. If 20% of the mixture was taken out and 10 liters of water was added. Find the amount of water in the mixture.

  1. 60

  2. 50

  3. 70

  4. 80

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

In 170L mixture (milk:water = 12:5), total parts = 17. Milk = (12/17)×170 = 120L, Water = (5/17)×170 = 50L. 20% removed: 34L taken out (milk removed = 24L, water removed = 10L). Remaining: Milk = 96L, Water = 40L. Add 10L water: Final water = 40+10 = 50L. Option B is correct.

Multiple choice

24 liters of a mixture contain milk and water in the ratio of 1: 5. If 6 liters of the mixture are replaced by 6 liters of milk. Find the ratio of milk to water in the new mixture?
  1. $4:5$
  2. $3:5$
  3. $7:3$
  4. $2:3$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture (24L at 1:5): Milk = 4L, Water = 20L. Removing 6L removes: Milk = 6 × (1/6) = 1L, Water = 6 × (5/6) = 5L. Remaining: Milk = 3L, Water = 15L. Adding 6L milk: Final Milk = 9L, Final Water = 15L. Ratio = 9:15 = 3:5 (option B).

Multiple choice

In a mixture of water and salt, water is 60%. When 40 liter water is added in the mixture ratio of water and salt becomes 5:3, find the initial quantity of the mixture.

  1. 240 liters

  2. 360 liters

  3. 450 liters

  4. 600 liters

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

Initial mixture has 60% water, so 40% salt. Let initial quantity = x. Salt = 0.4x. After adding 40 L water, total = x + 40, and water:salt = 5:3, so salt = 3/8 × (x + 40). Since salt amount unchanged: 0.4x = 3/8 × (x + 40). 0.4x = 0.375(x + 40). 0.4x = 0.375x + 15. 0.025x = 15. x = 600.

Multiple choice

Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Water. In which 40 kg of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Water in vessel B is 16: 19?

  1. 120

  2. 80

  3. 100

  4. 150

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

Let x be initial quantity of each vessel. Vessel A: 60% sugar, 40% water. Vessel B: 40% sugar, 60% water. After removing 40 kg from A (containing 24 kg sugar, 16 kg water) and adding to B: Vessel B has (0.4x + 24) kg sugar and (0.6x + 16) kg water. The ratio 16:19 means (0.4x + 24)/(0.6x + 16) = 16/19. Cross-multiplying: 7.6x + 456 = 9.6x + 256, giving 2x = 200, so x = 100. Option C is correct.

Multiple choice

In a solution ratio of liquid A and liquid B is 3 : 5. When 24 litre of liquid B is poured in the solution new ratio of solution A and B becomes 1 : 3. Find the initial quantity of solution. एक विलयन में द्रव A तथा B का अनुपात 3 : 5 है। जब 24 लीटर द्रव B मिश्रण में मिलाया गया तो द्रव A तथा B का नया अनुपात 1 : 3 हो जाता है। विलयन की प्रारम्भिक मात्रा ज्ञात कीजिए।

  1. 36

  2. 60

  3. 48

  4. 42

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

Let initial quantities be 3x and 5x (total 8x). After adding 24L of B: 3x : (5x + 24) = 1 : 3. Therefore: 3x/(5x + 24) = 1/3, so 9x = 5x + 24, giving 4x = 24 and x = 6. Initial total = 8x = 48L. Option C (48) is correct.