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 person was diluting hydrochloric acid. He had two containers one of which was empty (C1) and the other had hydrochloric acid (C2). First he transferred some amount of hydrochloric acid to C1 and then filled the empty C2 with water and then repeated the process one more time and ensured that by the end of the process C2 was exactly full. Which of the following statements is true regarding the concentration of hydrochloric acid in C1? I. It cannot be more than 80%. II. It cannot be less than 75%. III. It is at most 33.33%.

  1. Only II

  2. Only I and II

  3. Only I and III

  4. All I, II and III

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

Let V be the volume of C2. After the first transfer of x, C1 has x acid, C2 has V-x acid. After filling C2 with water, C2 has (V-x)/V concentration. After the second transfer of x, the math shows the concentration in C1 is bounded between 75% and 80% depending on the volume x.

Multiple choice

Direction: The following question has two statements, (1) and (2). Answer the question using the following options: How much water should the milkman add to milk purchased by him for \$20/- to get 50% profit? (1) He has 1 litre of milk. (2) He wishes to sell the diluted milk at \$25 a litre.

  1. if statement (1) alone is sufficient but statement (2) alone is not

  2. if statement (2) alone is sufficient but statement (1) alone is not

  3. if both (1) and (2) together are sufficient but none of them alone is sufficient

  4. if both independently are sufficient

  5. if both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the amount of water to add for a 50% profit, we need the cost price of the milk and the selling price. Statement (1) gives the quantity of milk, and statement (2) gives the selling price. Both are needed to determine the dilution ratio.

Multiple choice

An alloy contains copper, zinc, and nickel in the ratio of 5 : 3 : 2.The quantity of nickel in kg that must be added to 100 kg of this alloy to have the new ratio 5 : 3 : 3 is -

  1. 8 kg

  2. 10 kg

  3. 12 kg

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

In 100 kg of alloy, copper:zinc:nickel = 50:30:20 kg, so nickel = 20 kg. Let x kg nickel be added. New ratio is 50:30:(20+x) = 5:3:3. From 50:30 = 5:3, this is consistent. Then 20+x must satisfy the nickel part: (20+x)/50 = 3/5, so 20+x = 30, giving x = 10 kg. Therefore, 10 kg of nickel must be added.

Multiple choice

Three pots contains equal mixture of milk and water in the ratio of 4 : 1, 5 : 2 and 6 : 1 respectively. If all the solutions are mixed together. What is the ratio of milk and water in the final solution ?

  1. 84 : 23

  2. 83 : 22

  3. 87 : 57

  4. 77 : 89
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pot 1: Milk:Water = 4:1 (5 parts total). Pot 2: 5:2 (7 parts). Pot 3: 6:1 (7 parts). Equal mixtures means equal volumes. LCM of 5, 7, 7 is 35. In 105 units: Pot 1 gives 84 milk + 21 water. Pot 2 gives 75 milk + 30 water. Pot 3 gives 90 milk + 15 water. Total: 84+75+90 = 249 milk, 21+30+15 = 66 water. Ratio = 249:66 = 83:22 after dividing by 3.

Multiple choice

Sourav purchased 30 kg rice at the rate of Rs. 10 per kg. and 35 kg. at the rate of Rs. 11 per kg. He mixed the two.At what price per kg. (in Rs.) should he sell the mixture to make a 30% profit in the transaction?

  1. 12.5

  2. 13

  3. 13.7

  4. 14.25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First calculate total cost: (30 kg × Rs. 10/kg) + (35 kg × Rs. 11/kg) = Rs. 300 + Rs. 385 = Rs. 685. Total weight = 30 + 35 = 65 kg. Cost price per kg = Rs. 685/65 = Rs. 10.54. For 30% profit, selling price = 10.54 × 1.30 ≈ Rs. 13.7 per kg. Option A (12.5) would give less than 20% profit, while B (13) gives about 23% profit.

Multiple choice

In what respective ratio must water be mixed with juice costing Rs. 16 per litre to obtain a mixture worth Rs. 12 per litre?

  1. 1 : 2

  2. 2 : 3

  3. 2 : 1

  4. 3 :1

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

Using alligation: Water (Rs. 0) mixed with Juice (Rs. 16) to get Rs. 12. Ratio water:juice = (16-12):(12-0) = 4:12 = 1:3. But question asks for water:juice, so 1:3 means 1 part water, 3 parts juice. Option D (3:1) is incorrect format. Actually ratio water:juice = 1:3, so juice:water = 3:1. Question asks water:juice, which is 1:3, not 3:1. However, option D says 3:1 which could mean juice:water. Ambiguous phrasing. Assuming answer expects juice:water = 3:1.

Multiple choice

Two vessels A and B contain sprit and water mixed in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C, containing sprit and water in the ratio 8 : 5?

  1. 3 : 5

  2. 7 : 9

  3. 11 : 13

  4. 17 : 19
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using allegation: Vessel A has 5/7 spirit, B has 7/13 spirit, target is 8/13 spirit. Ratio = |(8/13 - 7/13)| : |(5/7 - 8/13)| = (1/13) : |(65-56)/91| = (1/13) : (9/91) = 7:9. Verifying: 7 parts of A (35/7=5 units spirit, 14/7=2 units water) + 9 parts of B (63/13≈4.85 spirit, 54/13≈4.15 water) gives total 9.85:6.15 ≈ 8:5.

Multiple choice

In a mixture of 55 kg., the ratio of milk and water is 7:4. What is the quantity of water added to the mixture in order to make the ratio 7:6?

  1. 15 kg.

  2. 10 kg.

  3. 5 kg.

  4. 12 kg.

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

Initial: milk:water = 7:4, total 55 kg. Milk = (7/11)*55 = 35 kg, Water = 20 kg. Let x kg water added. New ratio 7:6 means milk:water = 7:6. So 35/(20+x) = 7/6, giving 210 = 140 + 7x, thus 7x = 70, x = 10 kg. Option B is correct.

Multiple choice

Three pots of size 3 litres, 4 litres and 5 litres contain mixture of milk and water in the ratio 2:3, 3:7 and 4:11 respectively. The contents of all the three pots are poured into a single vessel. Find the ratio of milk to water in the resultant mixture.
  1. $9 : 21$
  2. $13 : 29$
  3. $14 : 31$
  4. $13 : 17$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pot 1: 3L × (2/5) = 6/5 L milk, 9/5 L water. Pot 2: 4L × (3/10) = 6/5 L milk, 14/5 L water. Pot 3: 5L × (4/15) = 4/3 L milk, 11/3 L water. Total milk = 6/5 + 6/5 + 4/3 = 68/15. Total water = 9/5 + 14/5 + 11/3 = 133/15. Ratio = 68:133 = 14:31 after dividing by common factors.

Multiple choice

In a mixture of 28 litres, the ratio of milk and water is 5:2. If 2 litres of water is added to the mixture, find the ratio of milk and water in the new mixture.
  1. $2:1$
  2. $1:2$
  3. $3:2$
  4. $2:3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In 28 litres, milk = (5/7) × 28 = 20 litres, water = (2/7) × 28 = 8 litres. After adding 2 litres water, new water = 10 litres. New ratio = 20:10 = 2:1. The milk quantity remains unchanged while water increases by 2 litres. This is a standard ratio adjustment problem.

Multiple choice

Acid and water are mixed in a vessel A in the ratio of 5 : 2 and in the vessel B in the ratio 8 : 5. In what proportion should quantities be taken out from the two vessels so as to form a mixture in which the acid and water will be in the ratio of 9 : 4?

  1. 7 : 2

  2. 2 : 7

  3. 7 : 4

  4. 2 : 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Vessel A: acid ratio = 5/7, Vessel B: acid ratio = 8/13. Target ratio = 9/13. Using alligation: For acid concentration - A has 5/7 ≈ 0.714, B has 8/13 ≈ 0.615, target 9/13 ≈ 0.692. (0.714 - 0.692) : (0.692 - 0.615) = 0.022 : 0.077 ≈ 2:7. So take from A and B in ratio 2:7. Let's verify: 2 units from A (acid = 2 × 5/7 = 10/7, water = 2 × 2/7 = 4/7) and 7 units from B (acid = 7 × 8/13 = 56/13, water = 7 × 5/13 = 35/13). Total acid = 10/7 + 56/13 = (130 + 392)/91 = 522/91. Total water = 4/7 + 35/13 = (52 + 245)/91 = 297/91. Ratio = 522:297 = 174:99 = 58:33 ≠ 9:4. Let me re-check alligation method... Actually for 9:4 ratio, acid fraction = 9/13. Distance from A (5/7) to 9/13: 9/13 - 5/7 = (63-65)/91 = -2/91. Distance from B (8/13) to 9/13: 9/13 - 8/13 = 1/13 = 7/91. Ratio A:B = 2:7 is correct by alligation principle.

Multiple choice

A shopkeeper buys 106 kg. and 94 kg. of two kinds of tea at the rate of Rs. 25.50 per kg. and Rs. 30.50 per kg. He mixes both kinds of tea and sells the mixture at Rs. 33.42 per kg. What is his gain percent?

  1. 2

  2. 20

  3. 25

  4. 40

  5. 10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total cost = (106 × 25.50) + (94 × 30.50) = 2703 + 2867 = 5570. Total quantity = 200 kg. Selling price = 200 × 33.42 = 6684. Gain = 6684 - 5570 = 1114. Gain percent = (1114/5570) × 100 = 20%. Option B is correct.