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

Glass A is filled with 2/3rd of wine and the remaining portion is filled with water. Similarly, glass B of same size is filled with 4/7th of wine and remaining with water. The contents of the two glasses are poured in a tumbler and mixed. The ratio of water to wine in the tumbler is:

  1. 2 : 3

  2. 5 : 7

  3. 7 : 9

  4. 8 : 13

  5. 9 : 14
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Glass A: Wine = 2/3, Water = 1/3. Glass B: Wine = 4/7, Water = 3/7. Total Wine = 2/3 + 4/7 = (14+12)/21 = 26/21. Total Water = 1/3 + 3/7 = (7+9)/21 = 16/21. Ratio of Water to Wine = (16/21) / (26/21) = 16/26 = 8/13.

Multiple choice

The ratio of milk and water in a container is 5 : 23. Some amount of water is added to increase the quantity of mixture by 25%, after which 20% of the mixture is removed and replaced with pure milk. The new ratio of milk to water is

  1. 10 : 24

  2. 11 : 24

  3. 12 : 24

  4. 13 : 24

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

Initial ratio 5:23 (Total 28 parts). Adding water increases total by 25%, so total becomes 28 * 1.25 = 35. The added 7 parts are water. New ratio: 5 milk, 30 water. Removing 20% of mixture (7 units) removes 1 milk and 6 water. Remaining: 4 milk, 24 water. Replacing with 7 units of pure milk results in 11 milk and 24 water.

Multiple choice

9 litres of milk is drawn from a cask full of milk and replaced with water. Again, 9 litres of the mixture is drawn from the cask and replaced with water. As a result, the ratio of milk to water in the resulting mixture becomes 16 : 9. Find the capacity of the cask.

  1. 65 litres

  2. 63 litres

  3. 46 litres

  4. 45 litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let capacity be C. After 2 operations, milk remaining = C * (1 - 9/C)^2. Ratio of milk to total = 16/25. (1 - 9/C)^2 = 16/25. 1 - 9/C = 4/5. 9/C = 1/5. C = 45.

Multiple choice

The percentage amounts of an acid in three solutions form a geometric progression. If we mix the first, second and third solutions in the ratio 3 : 2 : 1 by weight, we get a solution containing 22% acid. On the other hand, if we mix the solutions in the ratio 2 : 3 : 4 by weight, we obtain a solution containing 32% acid. Find the percentage of acid in each solution.

  1. 8%, 16%, 32%

  2. 27%, 9%, 3%

  3. 12%, 24%, 48%

  4. 44%, 22%, 11%

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

Let the percentages be a/r, a, ar. Using weighted averages: (3(a/r) + 2a + 1(ar)) / 6 = 22 and (2(a/r) + 3a + 4(ar)) / 9 = 32. Solving this system yields a=24, r=0.5 or r=2. The sequence is 12, 24, 48.

Multiple choice

We have two solutions of milk - A and B. Solution A contains milk and water in the ratio of 1 : 3 and solution B contains the same in the ratio of 2 : 3. If we mix both in equal quantities, then what is the ratio of milk and water in the new solution?

  1. 13 : 27

  2. 13 : 15

  3. 27 : 15

  4. 1 : 9

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

Solution A: 1/4 milk, 3/4 water. Solution B: 2/5 milk, 3/5 water. Mixing equal quantities: Milk = 1/4 + 2/5 = 13/20. Water = 3/4 + 3/5 = 27/20. Ratio = 13:27.

Multiple choice

We have three solutions of milk A, B and C. Solutions A, B and C contain milk and water in the ratios of 1 : 3, 2 : 3 and 3 : 2, respectively. If we mix them in the ratio 1 : 2 : 3, respectively, then what is the ratio of milk and water in the new solution?

  1. 19 : 20

  2. 19 : 21

  3. 5 : 13

  4. 19 : 5

  5. 1 : 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Difference between CI and SI for 2 years = P * (r/100)^2. 100 = P * (5/100)^2 = P * (1/20)^2 = P / 400. P = 100 * 400 = 40000.

Multiple choice

Two equal containers are filled with a mixture of water and alcohol. One of them contains three times as much alcohol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to alcohol is 3 : 2. Find the ratio of water to alcohol in each of the original containers.

  1. 2 : 1, 3 : 4

  2. 1 : 3, 1 : 2

  3. 2 : 3, 4 : 1

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

Let the containers have total volume V. Container 1 has alcohol A1 and water W1. Container 2 has alcohol A2 and water W2. Given A2 = 3A1. After mixing, total water/total alcohol = 3/2. Solving the ratios leads to the original compositions.

Multiple choice

The ratio of alcohol to water in a mixture of 170 ml is 7 : 10. When some amount of alcohol was added, the ratio of alcohol to water increased by 25%. The amount of alcohol added is

  1. 18.4 ml

  2. 15.5 ml

  3. 20.4 ml

  4. 17.5 ml

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

Initial mixture: 170 ml, ratio 7:10. Alcohol = 70 ml, Water = 100 ml. New ratio of alcohol to water increases by 25% of the original ratio (7/10 * 1.25 = 8.75/10). New alcohol amount = 8.75/10 * 100 = 87.5 ml. Added alcohol = 87.5 - 70 = 17.5 ml.

Multiple choice

A shopkeeper pays Rs. 20 per litre of milk. He adds water and sells the mixture at Rs. 25 per litre, thereby making 30% profit. The ratio of water to milk received by the customers is:

  1. 1 : 25

  2. 25 : 1

  3. 2 : 25

  4. 4 : 25

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

Let the cost price of milk be 20 and the selling price be 25. A 30% profit on cost means the effective cost of the mixture is 25/1.3 = 19.23. Using the alligation rule, the ratio of water (cost 0) to milk (cost 20) is (20 - 19.23) / (19.23 - 0) = 0.77 / 19.23, which simplifies to 1/25.