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IBPS RRB PO Mixture & Alligation

Study Material — 13 PYQs (2022–2022) · Concept Notes · Shortcuts

IBPS RRB PO Mixture & Alligation is a frequently tested subtopic — 13 previous year questions from 2022–2022 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

IBPS RRB PO Mixture & Alligation — Past Exam Questions

13 questions from actual IBPS RRB PO papers · all shown free · click option to reveal solution

Exam Q 12022Previous Year Pattern

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

Exam Q 22022Previous Year Pattern

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 make a 25% profit?

Exam Q 32022Previous Year Pattern

A mixture of 60 litres contains milk and water in the ratio 2:1. How much water should be added to make the ratio 1:1?

Exam Q 42022Previous Year Pattern

A chemist has two solutions of acid with concentrations 25% and 75%. In what ratio should they be mixed to obtain a 60% acid solution?

Exam Q 52022Previous Year Pattern

Two containers have alcohol solutions of 30% and 50% concentration respectively. In what ratio must they be mixed to obtain 40% concentration?

Exam Q 62022Previous Year Pattern

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?

Exam Q 72022Previous Year Pattern

A vessel contains 120 litres of a mixture of petrol and diesel in the ratio 7:5. How much of the mixture should be removed and replaced with pure petrol so that the ratio becomes 3:1?

Exam Q 82022Previous Year Pattern

Three containers have milk solutions with milk concentrations of 20%, 30%, and 50% respectively. They are mixed in the ratio 2:3:5. What is the milk concentration in the final mixture?

Exam Q 92022Previous Year Pattern

A goldsmith has two alloys of gold. The first alloy contains 60% gold and the second contains 80% gold. If he mixes them in the ratio 5:3, what is the percentage of gold in the resulting alloy?

Exam Q 102022Previous Year Pattern

A milkman mixes two types of milk: Type A costing ₹40 per litre and Type B costing ₹60 per litre. He sells the mixture at ₹55 per litre and makes a profit of 10%. If he prepares 100 litres of the mixture, how many litres of Type A milk did he use?

Exam Q 112022Previous Year Pattern

A jeweller has gold of two different purities: 18-carat (75% pure) and 22-carat (91.67% pure). He wants to create 240 grams of 20-carat gold (83.33% pure). How many grams of 18-carat gold should he use?

Exam Q 122022Previous Year Pattern

A chemist mixes three solutions with alcohol concentrations of 20%, 40%, and 60% in the ratio 2:3:5 respectively. He then removes 30% of the mixture and replaces it with a 50% alcohol solution. What is the final alcohol concentration in the mixture?

Exam Q 132022Previous Year Pattern

A merchant has two types of tea: Type P at ₹120 per kg and Type Q at ₹180 per kg. He mixes them and sells at ₹150 per kg. Due to wastage during packing, 5% of the mixture is lost. If he wants a profit of 20% on the cost price, what should be the ratio of Type P to Type Q in the mixture before packing?

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

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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