Mixture & Alligation Guide for RBI Grade B Phase 1 Exam

If we take a look at the RBI Grade B Phase 1 Quantitative Aptitude section of past years, questions on Mixture & Alligation usually appear 1 to 3 times (out of 30 questions). This makes up around 3% to 10% of the section. While the number seems small, the scoring potential is high because these questions are straightforward once you know the method. You just need to recall the right formula and set it up correctly. In this post, you’ll get the important concepts, the main alligation formula, and some fast tricks to solve such questions in seconds. By the end, you will be ready to tackle any Mixture & Alligation question with confidence.

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What Is Mixture & Alligation?

Mixture & Alligation is a method to quickly solve problems involving the mixing of two or more items with different prices, quantities, or concentrations to achieve a desired average.

You will mostly see two kinds of questions in RBI Grade B:

1. Price-based mixture – combining two types of commodities to get a target price.
2. Concentration-based mixture – mixing solutions with different concentrations of an ingredient (like milk and water problems).

Main Formula: Alligation Rule

When two items with values C1 and C2 are mixed to get a mean value M:

Quantity ratio = (C2 – M) : (M – C1)

Here:

• C1 = lower value
• C2 = higher value
• M = mean value

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Why This Is Important for RBI Grade B

The biggest advantage of alligation is speed. A normal average calculation takes more time, but the alligation rule gives you the ratio directly. This is exactly why exam setters use this topic — it tests both speed and understanding.

Important Formulas to Remember

• Weighted Average Formula:
  Average = (Sum of quantities × values) ÷ (Total quantity)
• Alligation Ratio Formula:
  Ratio = (High value – Mean value) : (Mean value – Low value)
• Pure to Mixture Replacement:
  If a quantity x is replaced from a mixture of volume V repeatedly:
  Final concentration = Initial concentration × (1 – x/V)^n

Types of Questions and Examples

Here are some types of questions that appear in the exam:

1. Price-Based Mixture

Example: A shopkeeper mixes tea worth ₹200/kg with tea worth ₹280/kg to get tea worth ₹240/kg. Find the ratio.

Using alligation:

High = 280, Low = 200, Mean = 240.

Ratio = (280 – 240) : (240 – 200) = 40 : 40 = 1 : 1.

2. Concentration-Based Mixture

Example: A container has 30 litres of milk (100%). How much water should be added to make it 80% milk?

Milk quantity stays 30.

Let total mixture be x.

80% of x = 30 ⇒ x = 37.5 litres.

Water = 37.5 – 30 = 7.5 litres.

3. Replacement Problem

Example: A vessel has 60 litres of milk. 6 litres are removed and replaced with water. This process is repeated 2 more times. Find remaining milk.

Formula: Final milk = 60 × (1 – 6/60)^3 = 60 × (0.9)^3 = 60 × 0.729 = 43.74 litres.

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5 Smart Tricks for Fast Solving

Some tricks make your calculations easy. Here are some tricks that will help you in solving all types of questions related to Mixture & Alligation:

1. Always place the mean in the middle: Draw the alligation cross with high value at top left, low value at bottom left, and mean in the middle right. The differences automatically give you the ratio.

2. For concentration, use percentage values directly: If milk = 100% and water = 0%, just put these into the alligation formula without converting to decimals.

3. For repeated replacement, don’t re-calculate each step: The (1 – x/V)^n formula directly gives you the final concentration. Saves time in multiple replacement questions.

4. Double-check ratios with a quick average: After finding the ratio, take the weighted average to confirm it matches the given mean. This prevents silly mistakes.

5. Learn to spot “hidden” alligation questions: Sometimes a question looks like average or ratio but can be solved in one step with alligation. This can save 30–40 seconds per question.

Practice Examples

Example 1:
Mix sugar worth ₹30/kg with sugar worth ₹45/kg so that mixture costs ₹40/kg.

Ratio = (45 – 40) : (40 – 30) = 5 : 10 = 1 : 2.

Example 2:
A solution has 20% alcohol. Another has 50% alcohol. In what ratio should they be mixed to get 40% alcohol?

Ratio = (50 – 40) : (40 – 20) = 10 : 20 = 1 : 2.

Example 3:
A 50-litre mixture has milk and water in ratio 3:2. 10 litres of mixture is replaced by pure milk. Find final ratio.

Milk = 30 litres, Water = 20 litres.
Remove 10 litres: milk removed = 6, water removed = 4.
Now milk = 24, water = 16. Add 10 litres milk → Milk = 34, Water = 16.
Ratio = 34 : 16 = 17 : 8.

Exam-Like Questions for Practice

Question 1: Mixture A contains milk and water in the ratio of 15:11 respectively while mixture B contains milk and water in the ratio of 13:9 respectively. Find the ratio in which mixture A should be mixed with mixture B so that ratio of milk to water in the resultant mixture becomes 7:5 respectively.

A) 17:11

B) 11:15

C) 12:11

D) 13:11

E) Can’t be determined

Question 2: 25% of a 320 litres mixture ‘A’ (milk and water) is drawn in container ‘P’. Mixture ‘B’ which contains milk and water, only in the ratio 3:5, respectively is also added to the container ‘P’ such that ratio of milk to water in container ‘P’ becomes 11:17. Which of the following can be possible quantity (in litres) of milk in mixture ‘A’ and mixture ‘B’?

A) 140 and 75

B) 120 and 60

C) 160 and 100

D) 200 and 40

E) 80 and 15

Question 3: Can ‘A’ contain mixture of milk and water, only such that quantity of milk is 120 litres more than that of water. 60% of the mixture from can ‘A’ is withdrawn in an empty can ‘B’. When ‘y’ litres of milk and (y + 12) litres of water is added to can ‘B’, the ratio of milk to water in it becomes 3:2. Find the sum of quantity of water withdrawn from can ‘A’ and quantity of milk added to can ‘B’.

A) 112 litres

B) 108 litres

C) 72 litres

D) 96 litres

E) Cannot be determined

Question 4: A mixture of milk and water contains ______% more milk than water in it. If the quantity of water would have been _____ litres more, then the quantity of milk would be ______% more/less than that of water. Initial quantity of mixture is 480 litres.

The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true:

I. 100, 40, 60

II. 40, 200, 30

III. 120, 50, 65

A) Only I

B) Only I and III

C) All I, II and III

D) Only II and III

E) Only II

प्रश्न 1: None

A) 17:11

B) 11:15

C) 12:11

D) 13:11

E) Can’t be determined

प्रश्न 2: None

A) 140 and 75

B) 120 and 60

C) 160 and 100

D) 200 and 40

E) 80 and 15

प्रश्न 3: None

A) 112 litres

B) 108 litres

C) 72 litres

D) 96 litres

E) Cannot be determined

प्रश्न 4: None

A) Only I

B) Only I and III

C) All I, II and III

D) Only II and III

E) Only II

ANSWER KEYS and SOLUTIONS:

Solution 1: D)

Quantity of milk in mixture A = 15/26 × total quantity of mixture A

Quantity of milk in mixture B = 13/22 × total quantity of mixture B

Quantity of milk in resultant mixture = 7/12 × total quantity of resultant mixture

By Alligation method we get;

Hence, option d.

Solution 2: A)

Let quantity of milk in mixture ‘A’ be ‘x’ litres

Therefore, quantity of water in mixture ‘A’ = (320 – x) litres

Let the quantity of milk and water in mixture ‘B’ be 3y litres and 5y litres, respectively

According to the question,

(0.25x + 3y)/{0.25(320 – x) + 5y} = 11/17

Or, 4.25x + 51y = 880 – 2.75x + 55y

Or, 7x – 880 = 4y

Or, y = 1.75x – 220

Putting x = 140 and y = 25, the above equation gets satisfied.

Therefore, quantity of milk in mixture ‘A’ and mixture ‘B’ is 140 litres and 75 litres, respectively

Hence, option a.

Solution 3: B)

Let the quantity of water in can ‘A’ be ‘x’ litres

Therefore, quantity of milk in can ‘A’ = (x + 120) litres

According to the question,

{0.6(x + 120) + y}/(0.6x + y + 12) = 3/2

Or, 1.2x + 144 + 2y = 1.8x + 3y + 36

Or, 0.6x + y = 108

Or, quantity of water withdrawn from can ‘A’ + quantity of milk added to can ‘B’ = 108 litres

Hence, option b.

Solution 4: C)

For I:

Let initial quantity of water in the mixture be ‘x’ ml

So, initial quantity of milk in the mixture = 2 × x = 2x ml

So, x + 2x = 480

Or, 3x = 480

Or, x = 160

Initial quantity of water in the mixture = x = 160 litres

Quantity of milk in the mixture = 2 × 160 = 320 litres

Final quantity of water = 160 + 40 = 200 litres

Required percentage = {(320 – 200)/200} × 100 = 60%

Therefore, ‘I’ is true.

For II:

Let initial quantity of water in the mixture be ‘x’ ml

So, initial quantity of milk in the mixture = 1.40 × x = 1.4x ml

So, x + 1.4x = 480

Or, 2.4x = 480

Or, x = 200

Initial quantity of water in the mixture = x = 200 litres

Quantity of milk in the mixture = 1.4 × 200 = 280 litres

Final quantity of water = 200 + 200 = 400 litres

Required percentage = {(400 – 280)/400} × 100 = 30%

Therefore, ‘II’ is true.

For III:

Let initial quantity of water in the mixture be ‘x’ ml

So, initial quantity of milk in the mixture = 2.2 × x = 2.2x ml

So, x + 2.2x = 480

Or, 3.2x = 480

Or, x = 150

Initial quantity of water in the mixture = x = 150 litres

Quantity of milk in the mixture = 2.2 × 150 = 330 litres

Final quantity of water = 150 + 50 = 200 litres

Required percentage = {(330 – 200)/200} × 100 = 65%

Therefore, ‘III’ is true.

Hence, option c.

How to Practise Mixture & Alligation Well

• Start with 5 basic price-based problems daily.
• Add 2 concentration-based problems once you’re confident.
• Include 1 replacement problem every alternate day.
• After solving, verify answers by the weighted average method.
• Time yourself. Keep it under 1 minute per question.

Daily Mini Task

1. Solve 5 alligation questions (mix price, concentration, and replacement).
2. Draw the alligation diagram each time until it becomes natural.
3. Verify answers with the weighted average method.
4. Write down any tricky steps that slowed you down.
5. Revise those points before you sleep.

Do this for 10 days in a row and you’ll notice your accuracy and speed improving.

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Takeaway

Mixture & Alligation may not dominate the RBI Grade B Quant section in terms of volume, but it’s one of the quickest scoring areas once you master the method. With daily practice, the alligation cross becomes second nature, and these questions will feel like free marks in the exam. Keep your formulas fresh, practise under timed conditions, and you’ll walk into the exam hall ready to turn these into quick wins.

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