Mixture and Alligation Question Sheet (Alligation)

Table Of Content

Practice Question

Answer Key

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Mixture and Alligation Question Sheet

Q.1 In a solution of acid and water, acid is 20% and in another solution acid is 35%. How many litres of the first solution must be added to 40 litres of the second solution to make a solution of 30% acid?

1. 15 L

2. 20 L

3. 21 L

4. 24 L

Q.2 A merchant has 1200 kg of sugar, part of which he sells at 9% profit and the rest at 15% profit. He gains 11% on the whole. The quantity (in kg) sold at 15% profit is:

1. 400 kg

2. 560 kg

3. 600 kg

4. 660 kg

Q.3 How many kgs of sugar at Rs.33 per kg must a person mix with 40 kg of sugar at Rs.20 per kg, so that on selling the mixture at Rs.30 per kg he gains 20% on the outlay? 

1. 20 kg

2. 25 kg

3. 30 kg

4. 35 kg

5. 50 kg

Q.4 Two mixtures of milk and water, having 58% and 85% milk concentration are mixed to get a mixture containing 70% milk. This mixture is then poured into a vessel containing 36 litres of water. It is found that the concentration of milk in the vessel is 50%. Find what amount of mixture(in litres) of 58% milk was used?

1. 90

2. 40

3. 50

4. None of these

Q.5 A milkman purchases milk at Rs.30 per litre and added 6 litres of water. By selling the resultant mixture at Rs.30 per litre, he made a profit of 15%. How many litres of milk did he buy initially?

1. 39L

2. 40L

3. 41L

4. 42L

5. 43L

Q.6 A examination is given by 80 students whose average score was 42 marks. If the average of the students who passsed the examination was 45 marks and those who failed was 35 marks. Then find the number of students who passed the examination.

1. 27

2. 28

3. 54

4. 56

Q.7 A fuel merchant purchased 20 litres of petrol at Rs.50 per litre and sold 12 litres of it at Rs.55 per litre. To the remaining petrol, he added 40% kerosene, the cost of which is Rs.20 per litre. If he sold this new mixture at the same rate at which he sold the first 12 litres, the total profit made by him would be

1. Rs.380

2. Rs.212

3. Rs.340

  .   d.    Rs.240

Q.8 A tank contains a mixture of water and milk. Total quantity of the mixture is 140L and the ratio of milk to water in the mixture is 9 : 5. If “X” L of the mixture is taken out and only 40L of water left in the mixture then what is the value of “X”?

1. 12 L

2. 24 L

3. 28 L

4. 36 L

Q.9 Pure milk costs Rs.12.60 per litre. A milkman adds water to 50 litres of pure milk and sells the mixture at Rs.10 per litre. If there is no profit and no loss for him, how many litres of water does he add?  

1. 10 litres

2. 13 litres

3. 15 litres

4. 16 litres

Q.10 A cricketer has a mean score of x runs in 10 innings. The ratio of run scored by him in 11th and 12th innings is 2:1. He scores 5x runs in 13th inning. If his mean score in 13 innings is 42 runs, what is the sum of the run scored by him in last two innings?

a.156

B. 182

C. 192

D. None of these

Q.11 One liter of liquid A weighs 2 kg, while one liter of liquid B weighs 1.5 kg. If the 800 ml of the mixture of liquid A and liquid B weighs 1.5 kg, what is the ratio of liquid A and liquid B in the mixture by volume?

1. 3 : 2

2. 1 : 3

3. 3 : 8

4. 3 : 1

Q.12 A mixture contains milk and water in the ratio 3 : 5. If 24 litres of pure milk is added to the mixture, the ratio of milk to water becomes 1 : 1.  How much water, in litres, should be added to the new mixture so that the ratio of milk to water becomes 3 : 5 again?

1. 24

2. 40

3. 33  

4. 48

Q.13 Solution 1 is a mixture of water and milk in the ratio 2 : 3 by volume. Solution 2 is a mixture of water and alcohol in the ratio 3 : 2 by volume. Solution 3 is a mixture of water and turpentine oil in the ratio 5 : 4 by volume. Solution 1, 2 and 3 are mixed in the ratio 9 : 5 : 4 by volume. Which of the following statements is not correct?

1. Total volume of water is less than 50% of the total volume of the final mixture.

2. 30% of the volume of the final mixture is milk.

3. Total volume of alcohol is less than 12% of the total volume of the final mixture.

4. 10% of the volume of the final mixture is turpentine oil.

Q.14 Two different types of cement type A and type B are mixed together. The type A cement costs Rs. 614 per kg, while the type B cement costs Rs. 695 per kg. By selling the mixture at a rate of Rs. 767 per kg a profit of 18% was earned. If the mixture contained 35 kg of type A cement, what is the amount of type B cement in the mixture?

1. 19 kg

2. 21 kg

3. 28 kg

4. 56 kg

Q.15 Consider three mixtures - the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4:3:2. Then the resulting mixture has

1. The same amount of water and liquid B

2. The same amount of liquids B and C

3. More water than liquid A

4. More water than liquid B

Q.16 An ‘x’ litre Solution having concentration of Sodium and Zinc in 2:3 ratio, is mixed with another ‘2x’ litre Solution having Sodium and Zinc in 3:2 ratio. The two Solutions are mixed and 40% of the mixture is replaced with pure Copper, then the percentage of Sodium in the final Solution will be

1. 30%

2. 32%

3. 36%

4. cannot be determined

Q.17 In two types of bronze, ratio of copper and tin are 7 : 3 and 13 : 7 respectively. The ratio in which these two types of bronze should be mixed, so that the ratio of copper and tin in this new type of bronze becomes 2 : 1 is

1. 1 : 2

2. 3 : 2

3. 3 : 4

4. 5 : 4

Q.18 The ratio of wine and water in container A is 2 : 3 and in container B is 3 : 5. Each container contains 40 liters mixture. If 20% quantity of container A mixed into container B, then how much quantity of water must be mixed in container B so that the ratio of wine and water becomes 1 : 2? 

1. 5.5 L

2. 5.9 L

3. 6.6 L

4. 7.2 L

Q.19 In two alloys, copper and zinc are present in the ratios of 4 : 1 and 1 : 3. 10 kg of 1st alloy 16 kg of 2nd alloy and some of pure copper are melted together. An alloy was obtained in which the ratio of copper to zinc was 3 : 2. Find the weight of the new alloy.

1. 34 kg

2. 35 kg

3. 36 kg

4. 38 kg

Q.20 There are two milk containers, each containing a solution of milk and water. In the first container, milk and water are in the ratio 5 : 3. Solutions from the first container and second container are mixed in the ratio 2 : 5. Milk and Water are in the ratio 17 : 11 in the resultant mixture. In the second container, the ratio of milk to water is

1. 2 : 3

2. 5 : 3

3. 3 : 5

4. 3 : 2

Q.21 The ratio of Milk and Water in a mixture is 4 : 5. If 9 litre Water is added to the mixture then the amount of whole mixture becomes 63 litre. Find the ratio of Milk and Water in the mixture after the addition of 9 litre of Water ?

1. 7 : 9

2.  9 : 7

3. 8 : 13

4. 13 : 8

Q.22 A man has milk worth Rs. 27 per liter and another worth Rs. 23 per liter. Equal quantities of these are mixed with water to obtain a mixture of 30 liters worth Rs. 20 per liter. Find how much water the mixture contains.

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Frequently Asked Questions — Mixture and Alligation for CAT & IPMAT 2026

What is the alligation rule?

Alligation gives the ratio in which two ingredients of different prices/concentrations must be mixed to get a desired mean value. Ratio = (C2 - Cm) : (Cm - C1), where C1 and C2 are the two component values and Cm is the mean/desired value. Draw the alligation cross to solve quickly.

How do I solve mixture problems involving replacement?

When a fraction f of a mixture is replaced by a pure component repeatedly n times: Final concentration = Initial concentration × (1 - f)^n. Example: 20L vessel of milk, 4L removed and replaced with water each time. After 3 replacements: milk% = (16/20)^3 = 0.512 = 51.2%.

What is the mean price / weighted average method?

The alligation rule is essentially weighted average. If two items cost C1 and C2 and are mixed in ratio m:n, mean cost Cm = (m×C1 + n×C2)/(m+n). Going in reverse: given Cm, C1, C2, find ratio m:n = (C2-Cm):(Cm-C1).

How do you solve a three-component mixture problem?

Break it into two alligation steps. First combine any two components to get an intermediate mixture, then use alligation with the third component to hit the target concentration. Alternatively use simultaneous equations if three components and two constraints are given.

What are milk-water mixture problems?

Standard form: a vessel contains x litres of milk. y litres are removed and replaced with water, repeated n times. Final milk = x × (1 - y/x)^n litres. These are the most common alligation problems in CAT and IPMAT — memorise this formula.

How is alligation used in profit/loss and percentage problems?

Alligation applies whenever you mix two groups with different rates: average salary, average speed, average marks, average price. If group A earns ₹40k and group B earns ₹60k, and average is ₹48k, ratio of A to B = (60-48):(48-40) = 12:8 = 3:2.

How many alligation questions appear in CAT?

Mixture and Alligation appears in 1-3 questions per CAT. It often combines with ratio-proportion, percentages, or profit-loss. IPMAT has 1-2 direct alligation questions. It is a must-do topic because the alligation technique is fast once mastered.

What is the key formula for successive dilution?

After n operations of removing r litres from a vessel of capacity V litres (initially pure) and replacing with another liquid: Fraction of original liquid remaining = ((V-r)/V)^n = (1 - r/V)^n. This is the single most tested alligation formula in competitive exams.