Mixture and alligation appears 2–4 times in SBI PO Prelims Quantitative Aptitude and is one of the most versatile topics in the entire syllabus. The same alligation method solves problems involving prices, concentrations, speeds, and ratios — yet most aspirants treat it as a single narrow topic and leave marks on the table.
The alligation method is faster than algebra for every mixture question type. Once you understand the cross-diagonal structure, you will rarely need to set up an equation — the diagram does the work.
- Mixture and alligation appears 2–4 times in SBI PO Prelims Quantitative Aptitude
- The cross-diagonal method finds mixing ratios in 3 steps without algebra
- The replacement formula — Final concentration = C × (1 − V/T)^n — solves repeated dilution questions directly
- Alligation applies beyond mixtures: price, speed, percentage, and ratio problems all use the same method
- Ten days of type-specific practice (15 questions/day) achieves full mastery
Source: SBI PO 2024 official exam pattern — sbi.co.in
✖️ The Cross-Diagonal Method: Your Core Alligation Tool
The cross-diagonal method is the fastest way to find the ratio in which two ingredients must be mixed to achieve a target mean value. It works for any two-component mixture question.
The 3-step process:
- Write the two component values (C1 and C2) on the left, with C1 on top and C2 on bottom
- Write the mean value (target) in the centre
- Subtract diagonally: Top right = C2 − Mean (ignore negatives, take absolute value). Bottom right = C1 − Mean
Mix milk at ₹20/litre and ₹35/litre to get ₹28/litre average. Ratio = (35−28) : (28−20) = 7 : 8
Preethi from Bengaluru cleared SBI PO 2024 after replacing her equation-based approach with cross-diagonal: "Mixture problems that took me 2 minutes now take 25 seconds. The diagram method removes all the algebra instantly."
🔄 The Replacement Formula: Solve Repeated Dilution Without Confusion
Replacement questions — where a fixed volume is repeatedly removed and replaced with water — confuse most aspirants because the concentration changes after each replacement. The standard algebraic approach requires multiple steps. The formula approach needs one.
Final quantity of original ingredient = Initial quantity × (1 − Volume removed / Total volume)^n
Where n = number of replacements.
💡 Example: A 40-litre vessel contains pure milk. 8 litres is removed and replaced with water, three times. Final milk = 40 × (1 − 8/40)³ = 40 × (0.8)³ = 40 × 0.512 = 20.48 litres
This formula works for any number of replacements and any vessel size.
📊 The 4 Application Areas of Alligation in SBI PO
Most aspirants know alligation for price-based mixture problems. SBI PO applies the same cross-diagonal method across four distinct question types:
| Application | What C1, C2 Represent | What Mean Represents |
|---|---|---|
| Price mixture | Cost price per unit of each ingredient | Target average cost price |
| Concentration mixture | % concentration of each solution | Target % concentration |
| Speed mixture | Speed of each part of journey | Overall average speed |
| Income/percentage | Two different rates or percentages | Combined average rate |
Source: SBI PO 2022–2024 paper analysis, bankersadda.com
Recognising which application type you're dealing with is the critical first step. All four use the identical cross-diagonal diagram — only the labels change.
📅 Your 10-Day Action Plan
- Days 1–3: Cross-Diagonal Drilling Practise price and concentration mixture questions using only the cross-diagonal method (15 questions/day). Draw the diagram for every question — even easy ones. Build the visual habit before adding complexity.
- Days 4–6: Replacement Formula Practice Drill replacement questions exclusively (15/day). Apply the formula directly — resist the temptation to work step-by-step for each replacement. Verify answers manually on Days 4–5 to build formula confidence.
- Days 7–10: Cross-Application Mixed Practice Mix all four application types (20 questions/day). Identify which application type you're facing within 10 seconds of reading the question. Target: under 40 seconds per question by Day 10.
📊 In our analysis of 500+ PrepGrind students, those who practised the cross-diagonal method across all four application types improved mixture and alligation accuracy from 57% to 90% within ten days (PrepGrind internal data, 2024).
🔍 People Also Search For
How to solve mixture and alligation problems quickly in bank exams?
Candidates can use the alligation method to compare ratios and find required mixture values easily. Understanding basic concepts like mean value, ratio, and weighted average helps in faster solving. Writing data in organised form reduces calculation errors. Regular practice improves speed and accuracy.
How to score 70 marks in SBI PO exam?
To score around 70 marks, candidates should focus on high-accuracy attempts and smart time management. Regular mock test practice, revision of arithmetic formulas, and strong basics in reasoning and quantitative aptitude are essential. Improving English comprehension and analysing mistakes after each test helps boost performance. Consistent preparation is important.
Is 60% necessary for SBI PO eligibility?
Eligibility for SBI PO mainly requires a graduation degree from a recognised university, and percentage criteria may vary according to official notification. Some recruitments may not require a fixed percentage for certain categories. Candidates should check the latest eligibility guidelines before applying. Proper awareness helps avoid application issues.
What is the formula used in mixture and alligation questions?
The alligation formula is used to find the ratio of two ingredients by comparing their values with the mean value. Candidates should understand cross-difference method and weighted average concepts. Learning these formulas helps in solving questions quickly. Regular revision improves calculation confidence.
How to prepare mixture and alligation topic for bank exams effectively?
Preparation should include practising basic to moderate level questions daily and revising important arithmetic concepts. Candidates should focus on improving calculation speed and avoiding lengthy methods. Sectional mock tests help in identifying weak areas. Consistent revision strengthens quantitative aptitude performance.
🎯 Conclusion: Your Next Step
Mixture and alligation for SBI PO becomes fully predictable once you recognise that the same cross-diagonal method applies to prices, concentrations, speeds, and percentages — and that the replacement formula covers all dilution questions in one step. Ten days of structured practice across all four application types converts this topic into a consistent full-marks contribution.
Ready to master SBI PO Quantitative Aptitude completely? Explore PrepGrind's SBI PO Quant module — featuring 350+ mixture and alligation drills across all question types, timed mock sets, and step-by-step video solutions built by Bank PO toppers.