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

There are two jars which have milk and water mixture in them. In the first jar, mixture of milk to water is 3 : 2 and in the second one, it is 4 : 5. If 5 litres of the first type is added to the 18 litres of the second type, what is the ratio of milk to water in the new mixture?

  1. 3 : 5

  2. 11 : 12

  3. 12 : 11

  4. 15 : 13

  5. 16 : 12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Jar 1: 5 litres, ratio 3:2 (3 litres milk, 2 litres water). Jar 2: 18 litres, ratio 4:5 (8 litres milk, 10 litres water). Total milk = 3 + 8 = 11. Total water = 2 + 10 = 12. Ratio = 11:12.

Multiple choice

A man purchases a variety of salt at Rs. 21 per kg and mixes it with 25 kg of another variety of salt at Rs. 12 per kg. If he gains 25% on selling the mixture at Rs. 20 per kg, then what was the quantity of salt that he purchased at Rs. 21 per kg?

  1. 15 kg

  2. 18 kg

  3. 20 kg

  4. 23 kg

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

Let x be the quantity of the first salt. Cost price = 21x + 12*25. Selling price = 20(x+25). Profit 25% means SP = 1.25 * CP. 20(x+25) = 1.25 * (21x + 300). 20x + 500 = 26.25x + 375. 125 = 6.25x. x = 125 / 6.25 = 20 kg.

Multiple choice

Some amount of acid is taken out of a 54 L vessel full of acid and then, an equal amount of water is added to it. The process is repeated once more. As a result, the vessel now contains 24 L pure acid. How much acid was taken out initially?

  1. 15 L

  2. 16 L

  3. 18 L

  4. 24 L

  5. 20 L
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the amount taken out. After two replacements, the remaining acid is 54 * (1 - x/54)^2 = 24. (1 - x/54)^2 = 24/54 = 4/9. 1 - x/54 = 2/3. x/54 = 1/3. x = 18.

Multiple choice

Manish purchases a particular variety of rice at Rs. 21 per kg and mixes it with 25 kg of another variety of rice purchased at Rs. 12 per kg. If he gains 25% on selling the mixture at Rs. 20 per kg, find the quantity of rice that he purchased at Rs. 21 per kg.

  1. 15 kg

  2. 18 kg

  3. 20 kg

  4. 23 kg

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

Let x be the quantity of rice at Rs. 21/kg. The total cost is 21x + (25 * 12). The total revenue from selling (x + 25) kg at Rs. 20/kg with a 25 percent gain is (Total Cost * 1.25) = 20(x + 25). Solving 1.25 * (21x + 300) = 20x + 500 leads to 26.25x + 375 = 20x + 500, so 6.25x = 125, giving x = 20 kg.

Multiple choice

65 L of a chemical P is mixed with 95 L of a chemical Q. If chemical P has sulphuric acid and hydrochloric acid in the ratio 3 : 2 and chemical Q has hydrochloric acid and sulphuric acid in the ratio 1 : 4, then the amount of hydrochloric acid in the new chemical mixture is

  1. 25 L

  2. 32 L

  3. 45 L

  4. 78 L

  5. 89 L
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Chemical P (65L): Acid P = 3/5 * 65 = 39L, Acid H = 2/5 * 65 = 26L. Chemical Q (95L): Acid H = 1/5 * 95 = 19L, Acid P = 4/5 * 95 = 76L. Total hydrochloric acid = 26 + 19 = 45L.

Multiple choice

In a tank containing 160 litres of solution, the ratio of milk to water is 5 : 3. Now, 40 litres of water is added to the tank. Then, 50 litres of solution is taken out and another solution of 50 litres, in which milk to water ratio is 9 : 1, is added to it. What is the ratio of milk to water in the final solution?

  1. 1 : 1

  2. 3 : 2

  3. 4 : 3

  4. 5 : 3

  5. 5 : 6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: 100M, 60W. Add 40W: 100M, 100W. Take 50L (ratio 1:1): 25M, 25W removed. Remaining: 75M, 75W. Add 50L (9:1): 45M, 5W added. Final: 120M, 80W. Ratio 120:80 = 3:2.

Multiple choice

Ishwar had a conical flask which was full of acid. Six litres of acid was removed and replaced by water. Again, 6 litres of the mixture was removed and replaced by water. The proportion of acid left in the flask then was 64/81 of the total mixture (in the flask). What is the capacity of the flask?

  1. 42 litres

  2. 48 litres

  3. 56 litres

  4. 54 litres

  5. 66 litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let capacity be V. After two replacements, acid remaining = V * (1 - 6/V)^2. Given (1 - 6/V)^2 = 64/81. Taking square root, 1 - 6/V = 8/9. 6/V = 1/9. V = 54.

Multiple choice

A salt trader buys two types of salt, the first type having price thrice that of the other. He sells the mixture at Rs. 18/kg, thus making a profit of 80%. If the ratio of mixing of the first type to second type of salt is 1 : 5, then find the cost price of the cheaper salt.

  1. Rs. 9.8/kg

  2. Rs. 9.5/kg

  3. Rs. 7.5/kg

  4. Rs. 8.5/kg

  5. Rs. 6.5/kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the cost price of the cheaper salt be x. Then the cost price of the costlier salt is 3x. The mixture ratio is 1:5, so the mean cost price is (1*3x + 5*x) / 6 = 8x/6 = 4x/3. Given the selling price is 18 with 80% profit, the cost price is 18 / 1.8 = 10. Setting 4x/3 = 10 gives 4x = 30, so x = 7.5.

Multiple choice

Cask I contains wine and water in the respective ratio 6 : 7 and cask II contains wine and water in the respective ratio 9 : 4. In what ratio must the contents of the two casks be mixed to get a mixture of wine and water in the respective ratio 8 : 5?

  1. 2 : 5

  2. 3 : 5

  3. 1 : 5

  4. 1 : 2

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

Using alligation: Wine in Cask I = 6/13, Wine in Cask II = 9/13, Mixture = 8/13. (9/13 - 8/13) : (8/13 - 6/13) = 1/13 : 2/13 = 1:2.

Multiple choice

There are two beakers I and II filled with 100 ml of alcohol and 100 ml of water, respectively. First, 10 ml of water is poured from beaker II into beaker I. Then, 11 ml of mixture from beaker I is poured back into beaker II. Then, from this new mixture in beaker II, 1 ml is poured back into beaker I. Which of the following statements is true?

  1. There is more water in beaker I than alcohol in beaker II.

  2. There is more alcohol in beaker I than water in beaker II.

  3. Neither 1 nor 2

  4. Both 1 and 2

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