Shortcut Techniques

Alligation or Mixture

Quantitative Aptitude Study Mode

Alligation or Mixture

⚡ Unlock time-saving calculation tricks and mental math techniques. Solve complex problems in seconds with proven shortcut methods used by top performers.

1 Exercises
15 Minutes
0% Completed
CALC + - ×

Shortcut Techniques

Study Material

Shortcut Techniques – Alligation or Mixture

Shortcut techniques in Alligation or Mixture help candidates solve concentration, ratio, replacement, and mixing problems quickly and accurately in SSC, Banking, Railway, Insurance, Defence, CAT, CDS, NDA, and various competitive examinations.

Most questions from this chapter are based on:

  • Alligation Rule
  • Mean Price Problems
  • Milk and Water Mixtures
  • Replacement of Liquids
  • Concentration and Dilution
  • Percentage-Based Mixtures

Learning shortcut methods reduces lengthy calculations and improves solving speed significantly.

Golden Rule of Alligation

Cheaper : Dearer

= (Dearer − Mean) : (Mean − Cheaper)

Shortcut #1: Cross Difference Method

This is the fastest method for solving alligation questions.

If:

  • Cheaper price = ₹20/kg
  • Dearer price = ₹30/kg
  • Mean price = ₹24/kg

Then: 

      30
        \
         \ 6
          \
           24
          /
         / 4
        /
      20

Required ratio:

= 6 : 4

= 3 : 2

✔ Always subtract diagonally in alligation.

Shortcut #2: Mean Always Lies Between Extremes

Remember:

Cheaper Price < Mean Price < Dearer Price

This helps eliminate wrong options quickly in MCQs.

Shortcut #3: Pure Substance Shortcut

Pure substance always means:

100% Concentration

Example:

  • Pure milk = 100% milk
  • Pure alcohol = 100% alcohol

Shortcut #4: Quantity of Substance Remains Constant

When water is added:

  • Total volume changes.
  • Original substance quantity remains unchanged.

This is one of the most important mixture concepts.

Shortcut #5: Percentage Formula Shortcut

Quantity of substance:

(x/100) × Total Volume

Example:

20% alcohol in 50 litres:

= (20/100) × 50

= 10 litres alcohol

Shortcut #6: Replacement Shortcut

If:

  • Total volume = x
  • y litres removed each time
  • n operations performed

Then:

Quantity Left

= Original × [(x − y)/x]n

This formula is extremely important for replacement questions.

Shortcut #7: Repeated Replacement Observation

Each replacement:

  • Reduces original substance.
  • Increases water proportion.
  • Follows exponential reduction.

Shortcut #8: Direct Ratio Shortcut

In alligation:

Difference from Mean

Becomes Opposite Ratio

Shortcut #9: Water Addition Shortcut

If water is added to milk:

  • Milk quantity remains constant.
  • Total mixture increases.
  • Milk percentage decreases.

Shortcut #10: Mixture Cost Shortcut

Mean price:

Total Cost / Total Quantity

Shortcut #11: Faster Ratio Simplification

Always simplify ratios immediately.

Example:

12 : 18 = 2 : 3

This saves time in further calculations.

Shortcut #12: Concentration Shortcut

New concentration after adding water:

New Percentage:

(Original Substance / New Volume) × 100

Shortcut #13: Average Shortcut in Mixtures

Alligation is based on weighted averages.

Use it whenever:

  • Price per kg
  • Speed per hour
  • Percentage
  • Average marks

are compared.

Shortcut #14: Equal Quantity Shortcut

If equal quantities are mixed:

Mean = Average of Prices

Example:

₹20/kg and ₹30/kg mixed equally:

Mean price:

= ₹25/kg

Shortcut #15: Quick Percentage Conversion

Percentage Fraction
10% 1/10
20% 1/5
25% 1/4
50% 1/2
75% 3/4

Useful for faster calculations.

Shortcut #16: Milk-Water Shortcut

If:

  • Milk = m litres
  • Water = w litres

Then:

Milk Percentage

= [m/(m+w)] × 100

Shortcut #17: Pure Liquid Reduction Shortcut

After each replacement:

  • Original liquid decreases proportionally.
  • Never becomes zero completely.

Shortcut #18: Alternate Mixing Shortcut

If multiple mixtures are combined:

  • Find quantity of pure substance separately.
  • Add them directly.
  • Then divide by total volume.

Shortcut #19: Quick Revision Formula Table

Concept Shortcut Formula
Alligation Ratio (d − m) : (m − c)
Mean Price Total Cost / Total Quantity
Substance Quantity (x/100) × Volume
Replacement Formula [(x−y)/x]n
Milk Percentage [m/(m+w)] × 100
Pure Substance 100%

Shortcut #20: Most Important Exam Tricks

  • Use cross-difference method directly.
  • Remember mean lies between extremes.
  • Use percentage-to-fraction conversion.
  • Focus on pure substance quantity.
  • Practice replacement problems regularly.
  • Avoid lengthy calculations.
  • Practice previous year aptitude questions.

Common Mistakes to Avoid

  • Using incorrect alligation ratios.
  • Confusing cheaper and dearer quantities.
  • Ignoring concentration changes.
  • Calculation mistakes in percentages.
  • Using wrong replacement powers.

Important Exam Tips

  • Memorize alligation formula thoroughly.
  • Practice percentage calculations daily.
  • Improve ratio simplification speed.
  • Use direct cross-difference method.
  • Focus on concentration concepts.
  • Practice milk-water problems regularly.
  • Practice previous year aptitude questions.

Shortcut techniques in Alligation or Mixture help candidates improve calculation speed, logical analysis, and accuracy in solving competitive examination aptitude questions efficiently.

0% read
Start First Exercise