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SBI PO Mixture & Alligation

Study Material — 5 PYQs (2021–2021) · Concept Notes · Shortcuts

SBI PO Mixture & Alligation is a frequently tested subtopic — 5 previous year questions from 2021–2021 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

SBI PO Mixture & Alligation — Past Exam Questions

5 questions from actual SBI PO papers · all shown free · click option to reveal solution

Exam Q 12021Previous Year Pattern

A chemist has two solutions of acid with concentrations 25% and 75% respectively. He mixes them to obtain 60 litres of 50% acid solution. How many litres of the 75% solution did he use?

Exam Q 22021Previous Year Pattern

A merchant has coffee of two qualities costing ₹180 per kg and ₹240 per kg. He wants to make a mixture of 40 kg at ₹210 per kg. How many kg of the cheaper coffee should he use?

Exam Q 32021Previous Year Pattern

A vessel contains 120 litres of a mixture of petrol and diesel in the ratio 7:5. How much pure petrol should be added to make the ratio 3:2?

Exam Q 42021Previous Year Pattern

Two alloys A and B contain copper and tin in the ratios 3:2 and 5:4 respectively. In what ratio should these alloys be mixed to get a final alloy with copper and tin in the ratio 4:3?

Exam Q 52021Previous Year Pattern

A merchant has two types of tea costing ₹80 per kg and ₹120 per kg. He mixes them and sells the mixture at ₹110 per kg, making a profit of 10%. In what ratio should he mix the two types of tea?

Concept Notes

Mixture & Alligation— Rules & Concept

Core ConceptRead this first — the foundation of the topic
CORE CONCEPT

Alligation is a quick method to find the ratio of mixing two items when we know their individual values and the mean (average) value of the mixture. It works on the principle that gain of one quantity equals loss of another quantity

KEY RULES

The ratio of quantities is inversely proportional to their differences from the mean 2. Cheaper quantity × Its difference from mean = Dearer quantity × Its difference from mean 3. For replacement problems, use: Final strength = Initial strength × (1 - R/C)^n where R = replaced quantity, C = total capacity, n = number of operations

Formula BlockMemorise — at least one formula appears in every paper
• Basic Alligation Formula: Ratio = (Mean - Cheaper value) : (Dearer value - Mean)
• For percentages: If x% and y% solutions are mixed to get z%, then Ratio = (z-x) : (y-z)
• Weighted Average: Mean = (A×a + B×b) / (A+B) where A,B are quantities and a,b are their values
• Replacement Formula: New concentration = Old × (1 - fraction removed)^number of operations
Exam PatternsWhat examiners ask — read before attempting PYQs

SSC CGL typically asks 1-2 questions on mixtures. Common types include: mixing two different priced items, alcohol-water mixtures, milk-water problems, successive mixing, and replacement of mixtures.

ShortcutsUse these to save 30–60 seconds per question

- CROSS METHOD: Draw a cross diagram. Put mean in center, cheaper value top-left, dearer value bottom-left. Differences go on right side.

This gives the mixing ratio directly.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Apply alligation formula Cheaper tea = Rs 64, Dearer tea = Rs 86, Mean = Rs 68

2
Step 2

Find differences Difference of cheaper from mean = 68 - 64 = 4 Difference of dearer from mean = 86 - 68 = 18

3
Step 3

Write ratio Ratio = 4:18 = 2:9 So tea worth Rs 64 and Rs 86 should be mixed in ratio 2:9. WORKED EXAMPLE 2: A vessel contains 60 litres of milk-water mixture with 80% milk. How much mixture should be removed and replaced with water to make milk 60%?

1
Step 1

Find initial milk quantity Initial milk = 60 × 80% = 48 litres

2
Step 2

Set up equation for final state Let x litres be removed and replaced with water Milk removed = x × 80% = 0.8x Final milk = 48 - 0.8x

3
Step 3

Apply condition Final milk percentage = 60% (48 - 0.8x)/60 = 60/100 48 - 0.8x = 36 0.8x = 12 x = 15 litres SHORTCUT FOR SUCCESSIVE OPERATIONS: When same fraction is removed repeatedly, use: Final = Initial × (1-f)^n where f = fraction removed, n = number of times.

Exam TrapsCommon mistakes students make — avoid these

#1: Students often confuse the direction of ratio in alligation. Remember: the ratio is OPPOSITE to what you might think. If mean is closer to cheaper value, you need MORE of the cheaper item, not less.

Always write (Mean - Cheaper) : (Dearer - Mean) for the ratio of Cheaper : Dearer.

Key Points to Remember

  • Alligation finds mixing ratios when individual values and mean value are known
  • Formula: Ratio = (Mean - Cheaper) : (Dearer - Mean) for quantities cheaper:dearer
  • Cross method: Put mean in center, write differences on opposite sides to get ratio
  • For replacement: Final concentration = Initial × (1 - removed fraction)^operations
  • In successive operations, multiply the reduction factor repeatedly
  • Weighted average formula: Mean = (Q1×V1 + Q2×V2)/(Q1+Q2)
  • The mixing ratio is inversely proportional to distance from mean value
  • When mean is closer to cheaper value, more cheaper quantity is needed
  • For percentage mixtures, treat percentages as values in alligation formula
  • Always check if final answer makes logical sense with given constraints

Exam-Specific Tips

  • Alligation rule: Cheaper quantity : Dearer quantity = (Mean - Cheaper value) : (Dearer value - Mean)
  • For milk-water problems, concentration typically reduces by factor (1 - R/C) per operation
  • When equal quantities of two mixtures are combined, resultant concentration is arithmetic mean of both
  • In successive mixing, final ratio = Product of individual operation ratios
  • Standard milk percentage in problems: Pure milk = 100%, typical mixtures = 80%, 75%, 60%
  • Replacement formula for n operations: Final = Initial × (1 - removed/total)^n
  • Cost price mixing follows same alligation rules as percentage mixing
  • Two mixtures of same concentration when mixed give same concentration
Practice MCQs

Mixture & Alligation — Practice Questions

7graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

A merchant has two types of sugar costing ₹20 per kg and ₹30 per kg. He mixes them and sells the mixture at ₹27 per kg, making a profit of 12.5%. In what ratio were the two types mixed?

Practice 2easy

A shopkeeper mixes two types of rice costing ₹40 per kg and ₹60 per kg in the ratio 3:2. What is the cost price of the mixture per kg?

Practice 3easy

A container has 120 litres of a mixture of petrol and diesel in the ratio 7:5. How many litres of diesel must be added to make the ratio 1:1?

Practice 4easy

Two containers have alcohol solutions of 30% and 50% respectively. In what ratio should they be mixed to get a 40% alcohol solution?

Practice 5easy

A goldsmith mixes gold of purity 80% with gold of purity 60% in the ratio 2:3. What is the purity percentage of the resulting mixture?

Practice 6medium

Two containers have alcohol solutions of strengths 30% and 50% respectively. In what ratio should they be mixed to get a 42% solution?

Practice 7medium

A shopkeeper mixes two types of rice costing ₹40 per kg and ₹60 per kg in the ratio 3:2. At what price per kg should he sell the mixture to gain 25% profit?

60-Second Revision — Mixture & Alligation

  • Formula: Ratio = (Mean - Cheaper) : (Dearer - Mean) - remember the cross pattern
  • Replacement: New concentration = Old × (1 - fraction removed)^number of times
  • Trap: Ratio direction is opposite to intuition - more cheaper when mean is closer to cheaper
  • Quick check: Final ratio quantities should be inversely related to their distance from mean
  • For successive operations, multiply the (1 - removed fraction) repeatedly
  • Cross method saves time: Draw cross, put mean center, differences give ratio directly
  • Always verify answer makes sense: percentages between 0-100, positive quantities
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