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

The ratio of milk and water in A and B is 5 : 3 and 4 : 3 respectively. The quantity of A and B is 40 lit and 84 lit respectively. After adding X lit of pure milk to mixture B the ratio of milk and water becomes 16 : 9. If A and B are mixed, what is the amount of milk in the final mixture?

  1. 84

  2. 150

  3. 120

  4. 89
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Mixture B has 84 liters with ratio 4:3 (48 milk, 36 water). Adding X liters of milk makes the ratio 16:9. (48+X)/36 = 16/9. 9(48+X) = 576, 432 + 9X = 576, 9X = 144, X = 16. Total milk = (5/8 * 40) + (48 + 16) = 25 + 64 = 89.

Multiple choice

How many kilograms of rice of Rs.5.4 per kg should be mixed with 10 kg of rice of Rs.4.5 per kg, such that there may be gain of 20% by selling the mixture at Rs.5.94 per kg.

  1. 10 kg

  2. 12 kg

  3. 15 kg

  4. 8 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the quantity of rice at Rs. 5.4/kg. The cost price of the mixture is (5.4x + 4.5*10) / (x + 10). To gain 20% at a selling price of 5.94, the cost price must be 5.94 / 1.2 = 4.95. Solving (5.4x + 45) / (x + 10) = 4.95 yields 5.4x + 45 = 4.95x + 49.5, so 0.45x = 4.5, giving x = 10 kg.

Multiple choice

A boy mixes milk and sugar in the ratio 2:3 in container 1 and milk and sugar in the ratio 4:1 in container 2. Find the ratio of milk to sugar of both container's mixtures are mixed in the ratio 2:1 ?

  1. 8:7

  2. 7:8

  3. 5:3

  4. 3:5

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

Container 1: Milk = 2/5, Sugar = 3/5. Container 2: Milk = 4/5, Sugar = 1/5. Mixed in 2:1 ratio: Milk = (2 * 2/5 + 1 * 4/5) / 3 = (4/5 + 4/5) / 3 = 8/15. Sugar = (2 * 3/5 + 1 * 1/5) / 3 = (6/5 + 1/5) / 3 = 7/15. Ratio = 8:7.

Multiple choice

A milkman sells milk at cost price, but he mixes water into it and thus gains 9.09%. The quantity of water in 1 litre of the mixture is

  1. 83.33 mL

  2. 90.90 mL

  3. 90.09 mL

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

A gain of 9.09% is equivalent to a fraction of 1/11, meaning the ratio of water to milk in the mixture is 1:11. In a 1-liter (1000 mL) mixture, the quantity of water is 1/12 of the total volume. Calculating 1000 / 12 gives approximately 83.33 mL.

Multiple choice

A cask contains lemon and sugar syrup in ratio of 7:3.A worker removes 30 litres of this mixture and if it is known that initial quantity of mixture was 150 litres. Then find the quantity in litres of lemon and sugar syrup respectively in the remaining mixture

  1. 84,36

  2. 90,30

  3. 75,45

  4. None of the above

  5. Can not be determine
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial: 150 liters, 7:3 ratio. Lemon = 105, Sugar = 45. Removing 30 liters (7:3 ratio) removes 21 liters lemon and 9 liters sugar. Remaining: Lemon = 105 - 21 = 84, Sugar = 45 - 9 = 36.

Multiple choice

A rice trader mixes 24 kg of rice priced at Rs 20/kg with 30 kg of rice priced at Rs 34/kg. If he sells the mixture at Rs 30/kg, find his profit or loss percentage.

  1. 8% Profit

  2. 8% Loss

  3. 7.4% Profit

  4. 7.4% Loss

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

Total cost = (24 * 20) + (30 * 34) = 480 + 1020 = 1500. Total weight = 24 + 30 = 54 kg. Total revenue = 54 * 30 = 1620. Profit = 1620 - 1500 = 120. Profit percentage = (120 / 1500) * 100 = 8%.

Multiple choice

A container contains 60 litres of milk. Some milk is replaced by water twice. Each time 12 litres of mixture is replaced. After the two replacements, what is the final ratio of milk to water?

  1. 16 : 9

  2. 18 : 7

  3. 17 : 3

  4. 11 : 4

  5. 15 : 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the formula for replacement, the final amount of milk is M = M_0 * (1 - x/V)^n. Here M_0 = 60, x = 12, V = 60, n = 2. M = 60 * (1 - 12/60)^2 = 60 * (0.8)^2 = 60 * 0.64 = 38.4. The amount of water is 60 - 38.4 = 21.6. The ratio of milk to water is 38.4 : 21.6 = 384 : 216 = 16 : 9.

Multiple choice

A 30-litre mixture of milk and water is in the ratio 2 : 1. 15 litres of the mixture is removed and replaced with pure milk. This process is repeated one more time. What is the final ratio of milk to water in the mixture?

  1. 10 : 1

  2. 7 : 5

  3. 8 : 3

  4. 11 : 1

  5. 15 : 7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial: 20L milk, 10L water. Removing 15L (half) leaves 10L milk, 5L water. Adding 15L milk makes it 25L milk, 5L water. Repeating: remove half (12.5L milk, 2.5L water) leaves 12.5L milk, 2.5L water. Adding 15L milk makes it 27.5L milk, 2.5L water. Ratio 27.5 : 2.5 = 11 : 1.

Multiple choice

Directions: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer: Ganpat is a oil trader, he mixes two varieties of oil in the ratio of 1 : 4. By selling the mixture at 14.40 per kg he gets a profit of more than 20%. Is the cost of the dearer variety, which is mixed, more than 20 per kg? Statement I: The cost of the cheaper variety of oil mixed is 10 per kg.Statement II: For every 1 kg of the cheaper variety of oil he mixed 4 kg of the dearer variety of oil.

  1. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question

  3. The data in statements I alone or in statement II alone is sufficient to answer the question.

  4. The data in both the statements I and II is not sufficient to answer the question.

  5. The data in both the statements I and II together is necessary to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. Find the quantity of milk in 180 L of mixture of milk and water. (1) If 24 L of mixture is replaced by equal quantity of water, then the ratio of milk and water in the mixture becomes 91 : 89. (2) If 12 L of mixture is replaced by equal quantity of milk, then the ratio of milk and water in the mixture becomes 11 : 7.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Both the statements alone are sufficient.

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

Both statements provide enough information to set up equations for the initial amounts of milk and water in the 180L mixture. Statement 1 allows solving for the initial ratio, and Statement 2 also allows solving for the initial ratio. Thus, both are independently sufficient.

Multiple choice

Directions: The following problem consists of a question followed by three statements (I), (II) and (III). You have to determine which statement(s) is/are sufficient/necessary to answer the question. A solution contains alcohol and water. What is the quantity of water in the solution? I. The ratio of alcohol to water in the solution is 1 : 2. II. If 150 ml of solution is replaced with alcohol, then the ratio of alcohol to water becomes 2 : 1. III. If 100 ml of soda is added to the solution, then the ratio of alcohol to solution becomes 1 : 4.

  1. Only I and II

  2. Only I and either II or III

  3. Only II and either I or III

  4. Any two statements

  5. All three statements
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I gives the ratio, but not the total quantity. Statement II allows calculating the total quantity by setting up an equation with the change in ratio. Statement III also allows calculating the total quantity. Thus, I and either II or III are sufficient.

Multiple choice

Directions: The question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and mark the correct answer. Jar A comprises a mixture of milk and water in the ratio of 3 : 2, respectively. Another mixture of milk and water is added to Jar A and the ratio of milk and water in the resultant mixture changes. What is the initial quantity of mixture present in Jar A? I. The ratio of milk and water in the mixture that is added to Jar A is 2 : 1, respectively. II. The ratio of the new quantities of milk and water in Jar A is 8 : 5, respectively. The quantity of water in the mixture added to Jar A was 6 litres.

  1. The data in both the statements I and II together is necessary to answer the question.

  2. The data in either statement I alone or statement II alone is sufficient to answer the question.

  3. The data in both the statements I and II together is not sufficient to answer the question.

  4. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  5. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find the initial quantity, we need the initial ratio (given as 3:2), the ratio of the added mixture (given in I), the final ratio (given in II), and the absolute quantity of one component added (given as 6 liters of water). All these pieces of information are required to set up and solve the system of equations.