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SSC CPO Mixture & Alligation

Study Material — 9 PYQs (2020–2020) · Concept Notes · Shortcuts

SSC CPO Mixture & Alligation is a frequently tested subtopic — 9 previous year questions from 2020–2020 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

SSC CPO Mixture & Alligation — Past Exam Questions

9 questions from actual SSC CPO papers · all shown free · click option to reveal solution

Exam Q 12020Previous Year Pattern

Two containers have milk and water in ratios 3:1 and 5:3 respectively. If equal quantities from each container are mixed together, what is the ratio of milk to water in the final mixture?

Exam Q 22020Previous Year Pattern

A shopkeeper mixes two types of rice costing ₹40 per kg and ₹60 per kg. In what ratio should they be mixed so that the cost of the mixture is ₹50 per kg?

Exam Q 32020Previous Year Pattern

A container has 120 litres of a solution with alcohol and water in ratio 7:5. How much pure alcohol must be added to make the ratio 3:1?

Exam Q 42020Previous Year Pattern

Three containers have solutions with salt concentrations of 20%, 30%, and 50% respectively. If equal volumes are mixed from all three, what is the salt concentration in the final mixture?

Exam Q 52020Previous Year Pattern

A chemist mixes two solutions of acid with concentrations 30% and 50%. If 40 litres of the first solution and 60 litres of the second solution are mixed, what is the concentration of acid in the resulting mixture?

Exam Q 62020Previous Year Pattern

A merchant has two types of rice costing ₹40 per kg and ₹60 per kg. He mixes them and sells the mixture at ₹55 per kg, making a profit of 10%. In what ratio should he mix the two types of rice?

Exam Q 72020Previous Year Pattern

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

Exam Q 82020Previous Year Pattern

A merchant mixes two types of rice costing Rs. 40 per kg and Rs. 60 per kg in a certain ratio. The cost price of the mixture is Rs. 50 per kg. Later, he adds 20 kg of the cheaper rice to 80 kg of the mixture. The new cost price per kg becomes Rs. 48. Find the original ratio of the two types of rice in the mixture.

Exam Q 92020Previous Year Pattern

A chemist has three solutions with acid concentrations of 20%, 30%, and 50% respectively. He mixes them in the ratio 2:3:5 to create a final solution. If the final solution has a total volume of 100 litres, what is the concentration of acid in the final mixture?

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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