SBI PO Mixture and Alligation Preparation Strategy 2026: Concepts, Tricks, Practice Questions + Free PDF

SBI PO Mixture and Alligation Preparation Strategy 2026: Mixture and Alligation is one of those arithmetic topics that looks intimidating in theory but becomes surprisingly fast once you understand the core method.

Most candidates skip it during preparation — and then spend 2–3 minutes struggling with it in the exam. That’s the wrong approach.

In SBI PO Prelims 2026, Mixture and Alligation appears as a part of the broader Arithmetic pool — and it shows up across standalone questions, word problems, and even inside DI sets. Knowing this topic well doesn’t just add direct marks. It speeds up your entire Quant section.

This guide covers every concept, the cross method explained simply, all question types with worked examples, common mistakes, and a daily practice routine so this topic is locked in before exam day.

2026 context: The SBI PO Notification 2026 is out with 1,500 vacancies. Prelims is in August 2026. The Quant section has 30 questions, 30 marks, 20 minutes. Arithmetic topics — including Mixture and Alligation — contribute 5–8 questions. Getting these right under time pressure starts with knowing the method cold.

Where Mixture and Alligation Fits in Quant

Before strategy, know the exam context.

Section	Questions	Marks	Time
Quantitative Aptitude	30	30	20 minutes

Mixture and Alligation in Quant 2026:

• Part of the Arithmetic pool — 5–8 questions total across all arithmetic sub-topics
• Expected standalone questions: 1–3 per paper
• Also appears embedded inside DI caselets and word problem sets
• Difficulty: Easy to Moderate in Prelims, Moderate to Hard in Mains
• Time target: 45–75 seconds per question

This topic also connects directly to Averages, Percentages, Profit & Loss, and SI/CI — which is why learning the alligation method unlocks shortcuts across multiple topics, not just this one.

For the full Quant topic breakdown and priority list, check Topics for Quant to Maximise Your SBI PO Prelims Score 2026.

Core Concepts — Understand These Before Anything Else

What Is a Mixture?

When two or more substances are combined, the result is a mixture. The key rule:

If a mixture of L litres contains two elements A and B in ratio p:q — and M litres of the mixture is removed — the ratio of A to B in those M litres is still p:q.

All mixtures are assumed homogenous (evenly distributed) unless stated otherwise.

What Is Alligation?

Alligation is a method to find the ratio in which two ingredients must be mixed to produce a mixture at a desired mean value.

It works for:

• Price (₹ per kg of different items)
• Concentration (% of solution)
• Speed (average speed problems)
• Percentage (weighted average of marks, interest rates, etc.)

The key formula:

Ratio = (Value of Dearer − Mean Value) : (Mean Value − Value of Cheaper)

This is the alligation rule. Everything else in this topic is a variation of it.

The Alligation Cross Method — Explained Simply

This is the one method you need to learn. It solves every basic alligation question in seconds.

How to draw it:

Cheaper (C)          Dearer (D)
     \                  /
      \                /
       Mean Value (M)
      /                \
     /                  \
(D − M)              (M − C)

The ratio of cheaper to dearer = (D − M) : (M − C)

Worked Example 1 — Price-Based Mixing

Rice costing ₹40/kg is mixed with rice costing ₹60/kg to get a mixture worth ₹48/kg. Find the ratio.

₹40                  ₹60
     \              /
          ₹48
     /              \
(60−48)=12      (48−40)=8

Ratio of cheaper (₹40) to dearer (₹60) = 12 : 8 = 3 : 2

Worked Example 2 — Concentration-Based Mixing

In what ratio should a 20% solution be mixed with a 50% solution to get a 30% solution?

20%                  50%
     \              /
          30%
     /              \
(50−30)=20      (30−20)=10

Ratio of 20% to 50% solution = 20 : 10 = 2 : 1

Practise this cross method until you can draw it and fill in the values in under 15 seconds. That’s the speed the exam demands.

All 6 Question Types in SBI PO — With Examples

Type 1 — Simple Mixing (Price or Concentration)

Two ingredients mixed to get a mean value. Find the mixing ratio.

Method: Alligation cross directly.

Example: Milk at ₹20/litre mixed with water (₹0) to get a mixture worth ₹16/litre.

₹0 (water)           ₹20 (milk)
        \            /
            ₹16
        /            \
    (20−16)=4    (16−0)=16

Ratio of water to milk = 4 : 16 = 1 : 4

Type 2 — Finding Quantity When Ratio Is Known

You know the mixing ratio and one quantity. Find the other.

Example: 3 kg of sugar at ₹40/kg is mixed with sugar at ₹60/kg to get a mixture at ₹45/kg. Find the quantity of the dearer sugar.

Step 1 — Apply alligation: Ratio of cheaper : dearer = (60−45) : (45−40) = 15 : 5 = 3 : 1

Step 2 — Use the ratio: Cheaper quantity = 3 kg → dearer quantity = 3 × (1/3) = 1 kg

Type 3 — Repeated Replacement (Mixture Withdrawn and Replaced)

This is the most commonly tested advanced type. A fixed quantity is withdrawn from a mixture and replaced with a pure ingredient — repeated n times.

Formula:

Final concentration of original ingredient = Initial quantity × [(1 − Quantity removed / Total quantity)^n]

Example: A 60-litre vessel has pure milk. 6 litres is removed and replaced with water. This is repeated twice. Find the milk remaining.

Final milk = 60 × (1 − 6/60)² = 60 × (54/60)² = 60 × (9/10)² = 60 × 81/100 = 48.6 litres

Step	Calculation	Result
Initial milk	60 litres	60 L
After 1st replacement	60 × (54/60)	54 L
After 2nd replacement	54 × (54/60)	48.6 L

Type 4 — Mixing Two Mixtures (Mixture of Mixtures)

Two vessels each contain a mixture of two elements in different ratios. A quantity from each is combined.

Method: Find the quantity of each element from both vessels separately, then combine.

Example: Vessel A has milk:water = 3:2. Vessel B has milk:water = 5:4. Equal quantities are mixed. Find the ratio in the final mixture.

• From A (per 5 parts): Milk = 3, Water = 2
• From B (per 9 parts): Milk = 5, Water = 4

Take LCM of 5 and 9 = 45 parts each:

• From A × 9: Milk = 27, Water = 18
• From B × 5: Milk = 25, Water = 20
• Total: Milk = 52, Water = 38
• Final ratio = 52 : 38 = 26 : 19

Type 5 — Alligation Applied to Averages / Weighted Mean

The alligation method works identically for averages — not just prices.

Example: A class of 40 boys has an average score of 55. A class of 60 girls has an average score of 45. Find the combined average.

55 (boys)            45 (girls)
     \              /
          M
     /              \
(M−45)           (55−M)

Ratio of boys to girls = 40:60 = 2:3

(M−45) : (55−M) = 2 : 3 3(M−45) = 2(55−M) 3M − 135 = 110 − 2M 5M = 245 M = 49

Type 6 — Profit Through Adulteration

A seller mixes a cheaper substance (often water at ₹0) with a pure item and sells at the original price. Find profit percentage.

Shortcut: Profit % = (Quantity of cheaper added / Quantity of original) × 100

Example: Milk worth ₹20/litre is mixed with water in ratio 4:1, and sold at ₹20/litre. Find profit %.

Water added per 5 litres = 1 litre Cost of 5 litres = 4 × 20 = ₹80 Selling price = 5 × 20 = ₹100 Profit % = (20/80) × 100 = 25%

All Formulas at a Glance

Concept	Formula
Alligation Rule	Ratio = (Dearer − Mean) : (Mean − Cheaper)
Repeated Replacement	Final = Initial × (1 − removed/total)ⁿ
Mixture of Mixtures	Calculate each element separately, then sum
Profit by Adulteration	Profit % = (Adulterant qty / Pure qty) × 100
Weighted Average	Apply alligation cross with group sizes as ratio

Common Mistakes Candidates Make

Mistake	Why It Happens	The Fix
Swapping cheaper and dearer in the cross	Rushing through the diagram	Always write Cheaper on left, Dearer on right — every time
Using SP instead of CP in price problems	Not reading the question carefully	Re-read the last line — check if mean value is CP or SP
Forgetting the ⁿ in repeated replacement	Treating each step separately	Write out the formula first, then substitute values
Wrong LCM in mixture of mixtures	Skipping the LCM step	Always find LCM of both total parts before combining
Applying alligation where weighted average is needed	Confusing the two methods	If group sizes are given, use weighted average formula
Spending 3+ minutes on a complex mixture problem	Not recognising the type fast	Identify question type in 10 seconds — skip if type isn’t clear

How Mixture and Alligation Connects to Other Topics

This is what makes this topic especially valuable. The alligation method is a universal shortcut that appears across multiple Quant topics.

Topic	How Alligation Helps
Averages	Find combined average of two groups using cross method
Profit & Loss	Find ratio of items at two prices for a target profit
Simple & Compound Interest	Find ratio of investments at two interest rates for mean return
Percentages	Mix two percentage values to reach a target percentage
Speed-Distance	Find average speed when two speeds and distances are given

Once you understand the alligation cross method, you’ll start spotting it in questions that don’t even mention “mixture.” That recognition alone saves 30–40 seconds per question.

The SBI PO preparation strategy after notification explicitly lists Mixture and Alligation as a core Arithmetic topic to cover alongside Profit & Loss, SI & CI, and Ratios — practice all of these together since they share methods.

Where Mixture and Alligation Sits in Your Quant Attempt Order

In the 20-minute Quant section, Arithmetic questions (including Mixture and Alligation) fall into the middle tier of your attempt sequence.

The right attempt order: Simplification/Approximation → Number Series → Quadratic Equations → Arithmetic (including Mixture & Alligation) → DI (last)

Attempt Arithmetic questions if the method is clear within 10 seconds. If a mixture problem looks like it involves repeated replacement with complex fractions — skip it in Round 1 and return only if time permits.

The full attempt order with time targets is in the SBI PO mock test attempt order strategy 2026.

For the skip-or-attempt decision across all Quant question types, the SBI PO mock accuracy strategy tells you exactly when to skip a Mixture question and when to back yourself.

Daily Practice Plan for Mixture and Alligation

Day	Topic	Questions
Day 1	Alligation cross method — price and concentration	20 questions
Day 2	Finding quantity when ratio is known	15 questions
Day 3	Repeated replacement formula	15 questions
Day 4	Mixture of mixtures (two vessels)	15 questions
Day 5	Alligation applied to averages and weighted mean	15 questions
Day 6	Profit through adulteration	10 questions
Day 7	Mixed practice — all types timed	25 questions under exam conditions
Day 8 onwards	5–10 Mixture questions daily alongside other arithmetic topics	Continuous

From Day 8, practise Mixture and Alligation questions mixed in with Percentage, Profit & Loss, and Averages. This simulates the real exam where you don’t know which arithmetic type is coming.

Use the SBI PO Previous Year Question Papers PDF for real exam-level Mixture and Alligation questions from 2023, 2024, and 2025 papers — these give you the most accurate picture of how SBI frames these problems.

Download: Free SBI PO Mixture and Alligation PDF 2026

What the free resource includes:

• All formulas and the alligation cross method — one-page quick reference
• 50 practice questions across all 6 question types
• Repeated replacement questions with step-by-step solutions
• Mixture of mixtures — 10 questions with detailed working
• Answer key with method explanation for every question

Download the Free Mixture and Alligation Questions PDF for SBI PO — the live quiz includes exam-oriented questions based on the latest SBI PO pattern, with solutions explained in detail.

For full Quant section practice with Mixture and Alligation in its real exam context, attempt a free SBI PO Mock Test on PracticeMock and check your Arithmetic accuracy in the section-wise analysis after the test.

FAQs

Q. How many Mixture and Alligation questions appear in SBI PO Prelims 2026?

Typically 1–3 standalone questions from this topic, plus additional appearances inside word problem sets and DI caselets. The broader Arithmetic pool contributes 5–8 questions total, and Mixture and Alligation is one of the most tested sub-topics within it.

Q. What is the alligation cross method?

It’s a visual shortcut for finding the ratio in which two ingredients must be mixed to produce a mean value. The formula is: Ratio = (Dearer − Mean) : (Mean − Cheaper). Draw a cross, put the cheaper value top-left and dearer top-right, mean in the centre, and cross-subtract diagonally to get the ratio.

Q. Is the alligation method only for price-based problems?

No — this is the most important thing to understand. The alligation method works for any weighted average situation: concentration of solutions, average marks of groups, average speed, interest rates, and more. The method is identical — only the values plugged in change.

Q. What is repeated replacement and when does it appear?

Repeated replacement questions describe a vessel where a fixed quantity of mixture is removed and replaced with a pure ingredient — repeated multiple times. The formula is: Final concentration = Initial × (1 − removed/total)ⁿ. This appears in both Prelims and Mains.

Q. How long should a Mixture and Alligation question take in the exam?

Target 45–75 seconds for standard questions using the alligation cross. Repeated replacement questions may take up to 90 seconds if the formula is applied correctly from the start. If a question isn’t clear within 15 seconds of reading — skip it.

Q. Should I use the alligation cross or the formula method? ‘

Use the alligation cross for all ratio-finding questions — it’s faster and more visual. Use the repeated replacement formula only for questions specifically describing the “withdraw and replace” process. The cross method cannot be applied to repeated replacement.

Q. Does Mixture and Alligation appear in SBI PO Mains?

Yes — and at a higher difficulty. Mains questions often combine mixture concepts with ratios, percentages, or involve three vessels instead of two. Mastering the Prelims-level concepts first is essential before attempting Mains-level variations.

Q. What’s the fastest way to improve at this topic?

Learn the alligation cross method on Day 1. Practise it on 20 price and concentration questions the same day. By Day 3, it becomes automatic. After that, add repeated replacement and mixture of mixtures as separate practice sessions. One week of focused daily practice is enough to make this topic reliable.

Related Blogs

Blog	What It Covers
SBI PO Syllabus 2026	Complete topic-wise breakdown for Prelims and Mains
SBI PO Notification 2026	1,500 vacancies, pattern changes, attempt limit, CTC updates
Topics for Quant to Maximise SBI PO Prelims Score	DI, Number Series, Simplification weightage and priority
Top 40 Missing Number Series with Examples	40 solved Number Series questions across all pattern types
SBI PO Mock Test Series 2026	Free first test, 20-min sectional Quant practice, All India Rank
SBI PO Mock Test Attempt Order Strategy	Where Number Series fits in your 20-minute Quant sequence
SBI PO Mock Accuracy Strategy	When to skip Number Series and when to attempt
SBI PO Mock Speed-Building Strategy	Calculation drills that support faster Number Series recognition
SBI PO Mock Time Management Strategy	How to allocate time within the 20-minute Quant section
SBI PO Mock Question Selection Strategy	Skip-or-attempt decision framework for all Quant topics
SBI PO Previous Year Question Papers PDF	Real exam Number Series questions from 2023–2025
SBI PO Section-Wise Preparation Plan 2026	Full Quant preparation strategy for Prelims 2026
How Many Questions to Attempt in SBI PO Prelims	Attempt targets — including how many Quant questions to attempt
SBI PO Cut Off 2026	Expected qualifying scores to set your Number Series accuracy target

Final Word

Mixture and Alligation is not a difficult topic. It’s an unfamiliar one — and familiarity comes from practice, not re-reading theory.

Learn the alligation cross on Day 1. Drill it on 20 questions. Add repeated replacement on Day 3. Mix all types from Day 7.

One focused week makes this topic automatic. After that, every Mixture and Alligation question in a mock test becomes a guaranteed mark — not a question you debate whether to attempt.

Start with the free Mixture and Alligation quiz on PracticeMock today. Then take a full SBI PO mock test to see how this topic fits into your real 20-minute Quant performance.

Disclaimer: Exam dates, question counts, and pattern details are based on the official SBI PO 2026 notification and data available at the time of writing. Always verify the latest updates on the official SBI website: www.sbi.bank.in