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 contain a mixture of milk and water. In one container, the ratio of milk to water is 4 : 1 and the ratio of milk to water in the other container is 1 : 3. 10 litres of mixture from the first container and 16 litres of mixture from the second container is mixed together in a third container, already containing some amount of pure milk. In the new mixture, it was found that the ratio of milk to water was 3 : 2. Find the volume of the new mixture.

  1. 30 litres

  2. 35 litres

  3. 40 litres

  4. 48 litres

  5. 52 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Container 1: 10L (8 milk, 2 water). Container 2: 16L (4 milk, 12 water). Total milk = 12 + pure milk M. Total water = 14. Ratio (12+M)/14 = 3/2. 24 + 2M = 42. 2M = 18, M = 9. Total volume = 10 + 16 + 9 = 35.

Multiple choice

A soft drink has an artificial flavour and a sweetener; it contains 16.67% artificial flavour. Another soft drink contains an artificial flavour and water in the ratio 4 : 6, respectively. These two drinks are mixed in the ratio 8 : 2. The quantity of sweetener is what percent of the quantity of artificial flavour in the final mixture?

  1. 312.5%

  2. 225.5%

  3. 265.2%

  4. 381.5%

  5. 325.7%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Drink 1: 16.67% (1/6) flavor, 5/6 sweetener/water. Drink 2: 4:6 flavor:water (0.4 flavor). Mix 8:2 ratio. Final mixture composition: (8/10 * 1/6 + 2/10 * 0.4) flavor. Sweetener is the remainder. Calculation yields 312.5%.

Multiple choice

A container is full of sugar syrup. 4 gallons of syrup is drawn out of the container and replaced with water. From this water-syrup mixture, 4 gallons of mixture is again withdrawn and replaced with water. The ratio of the sugar syrup to water in the container was then found to be 36 : 13. How many gallons does the container hold?

  1. 8 gallons

  2. 12 gallons

  3. 15 gallons

  4. 28 gallons

  5. 30 gallons
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let V be the total volume. After two operations, the fraction of syrup remaining is (1 - 4/V)^2. Given this equals 36/(36+13) = 36/49. Thus, 1 - 4/V = 6/7. 4/V = 1/7, so V = 28 gallons.

Multiple choice

Two samples of alloys containing silver and aluminium are marked as A and B. Sample A contains silver and aluminium in a ratio of 4 : 5 and sample B contains silver and aluminium in the ratio 5 : 1. We have to make another alloy using the alloys A and B, so that the ratio of silver to that of aluminium in the new alloy would be 5 : 4. Find the ratio of the alloy A to that of the alloy B, so that when mixed together, they achieve our aim.

  1. 5 : 3

  2. 5 : 1

  3. 1 : 2

  4. 5 : 2

  5. 2 : 5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Use alligation on silver content. A: 4/9, B: 5/6, Mix: 5/9. (5/6 - 5/9) / (5/9 - 4/9) = (15/18 - 10/18) / (1/9) = (5/18) / (2/18) = 5/2.

Multiple choice

Mixtures A and B are contained in two separate vessels. Mixture A contains ingredients P, Q and R in a ratio of 3 : 5 : 2 and mixture B contains ingredients P and Q in a ratio of 4 : 5. We have to make 540 litres of a new mixture by adding the mixtures A and B in a ratio of 1 : 2. What will be the quantity of ingredient P in the final mixture?

  1. 201 litres

  2. 210 litres

  3. 214 litres

  4. 231 litres

  5. 260 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total mixture = 540L. Ratio A:B = 1:2, so A = 180L, B = 360L. In A (ratio 3:5:2), P = 3/10 * 180 = 54L. In B (ratio 4:5), P = 4/9 * 360 = 160L. Total P = 54 + 160 = 214L.

Multiple choice

A flask contained a mixture of wine and water. It contained 30% wine and the rest was water. A person removed some part of the mixture and replaced it with another wine-water mixture, in which the wine was only 12%. The new mixture was then found to be containing 18% wine and rest was water. What part of the wine-water mixture was replaced?

  1. 2 3

  2. 1 3

  3. 1 2

  4. 5 6

  5. 7 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using alligation between the initial mixture (30% wine) and the replacing mixture (12% wine) to get the final mixture (18% wine): the ratio of initial mixture to replaced mixture is (18 - 12) : (30 - 18) = 6 : 12 = 1 : 2. This means 2 parts out of 3 parts total were replaced. Option A shows '2 3' representing 2/3.

Multiple choice

The ratios of spirit to wine in two flasks labelled as A and B, containing spirit and wine mixture, are 7 : 3 and 3 : 1, respectively. Some amounts of the mixtures from the two flasks are poured into a third flask. The new mixture now contains spirit and wine in the ratio of 11 : 4. Find the ratio in which the mixtures from the flask A and flask B are mixed together to get this new mixture.

  1. A : B = 1 : 2

  2. A : B = 2 : 1

  3. A : B = 1 : 3

  4. A : B = 2 : 3

  5. A : B = 3 : 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using alligation: Flask A has 7/10 spirit, Flask B has 3/4 spirit. The mixture has 11/15 spirit. Difference 1: |11/15 - 3/4| = |44/60 - 45/60| = 1/60. Difference 2: |7/10 - 11/15| = |21/30 - 22/30| = 1/30. Ratio = (1/60) : (1/30) = 1:2.

Multiple choice

A container contained 80 litres of a mixture of two liquids A and B. When 55% of the total mixture was drawn out, it was found that the drawn-out mixture contained 70% liquid A and 30% liquid B. What were the initial quantities of liquid A and liquid B in the container?

  1. A = 56 L, B = 24 L

  2. A = 55 L, B = 25 L

  3. A = 60 L, B = 20 L

  4. A = 30 L, B = 50 L

  5. A = 25 L, B = 55 L
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total mixture = 80L. 55% drawn = 44L. The drawn mixture has 70% A and 30% B. A drawn = 0.7 * 44 = 30.8L. B drawn = 0.3 * 44 = 13.2L. This implies the mixture was not uniform or the question implies the initial composition. If the mixture was 70% A and 30% B initially, A = 0.7 * 80 = 56, B = 0.3 * 80 = 24.

Multiple choice

Shilpa has a solution which contains 90% water and the rest is milk. Alka has 9 litres of solution which has 60% milk. They both mix their solutions. If the resultant solution has 40% milk, then how much litres of solution does Shilpa have?

  1. 4 litres

  2. 5 litres

  3. 6 litres

  4. 7 litres

  5. 8 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Shilpa have x litres of solution (10% milk). Alka has 9 litres (60% milk, so 5.4 litres milk). Total volume x+9, total milk 0.1x + 5.4. (0.1x + 5.4) / (x+9) = 0.4. 0.1x + 5.4 = 0.4x + 3.6. 1.8 = 0.3x, so x = 6.

Multiple choice

25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is in the ratio 1 : 2 and the amount of lead and tin in the alloy Y is in the ratio 2 : 3, then what is the ratio of lead to tin in the mixture?

  1. 1 : 2

  2. 2 : 3

  3. 3 : 5

  4. 7 : 11
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Alloy X: 25 kg, 1:2 ratio (8.33 kg lead, 16.67 kg tin). Alloy Y: 125 kg, 2:3 ratio (50 kg lead, 75 kg tin). Total lead = 58.33 kg, Total tin = 91.67 kg. Ratio = 58.33/91.67 = 7/11.

Multiple choice

A trader mixes some quantity of basmati rice costing Rs. 84 per kg with 35 kg of ordinary rice costing Rs. 48 per kg. If he sells the mixture at Rs. 80 per kg and makes a profit of 25%, then how much quantity of basmati rice does he mix?

  1. 25 kg

  2. 28 kg

  3. 30 kg

  4. 33 kg

  5. 35 kg
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the quantity of basmati rice. Total cost = 84x + 35*48. Total revenue = 80(x+35). Profit is 25%, so Revenue = 1.25 * Cost. 80(x+35) = 1.25 * (84x + 1680). 80x + 2800 = 105x + 2100. 700 = 25x, so x = 28.

Multiple choice

A compound contains zinc and bronze in the ratio of 5 : 2 and another compound contains zinc and bronze in ratio of 13 : 1. In what ratio must the two compounds be mixed to obtain a new compound containing zinc and bronze in the ratio of 6 : 1?

  1. 6 : 1

  2. 4 : 1

  3. 3 : 1

  4. 1 : 2

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

Using the method of alligation, the first compound has 5/7 zinc and the second has 13/14 zinc. The target mixture has 6/7 zinc. The differences are |13/14 - 12/14| = 1/14 and |10/14 - 12/14| = 2/14. The ratio is 1/14 : 2/14, which simplifies to 1 : 2.