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Back to Percentage Blueprint
Pattern 25·Hybrid·L3

Percentage + Average

High FrequencyMust Master 90–120 sec

USE WHEN

Group sizes and/or group averages differ by percentages.

BEST METHOD

Alligation Method

TARGET

90–120 sec

MASTERY

not started

Recognition Cues

  • group ratio + group average
  • overall average asked
  • higher/lower average by %

How to Recognise

Group sizes and/or group averages differ by percentages.

Core Concept

Use weighted averages after translating percentage relations into multipliers.

Combinedavg=Σ(niai)/ΣniCombined avg = Σ(nᵢaᵢ)/ΣnᵢCombinedavg=Σ(ni​ai​)/Σni​

Athena Shortcut

Alligation can solve reverse group-ratio questions faster.

Alternative Method · Alligation Method

For reverse-average cases, use alligation instead of the full weighted-average equation.

Timed drill

Identify the base or invariant before you calculate.

2:00

Attempt first · Standard Example

Group A avg=40, group B avg=60, equal sizes. Combined avg?

Attempt first · CAT-Level Example

Men:women=3:2. Men's average salary is 20% higher than women's. Overall average is ₹33,000. Find women's average.

Common Trap

  • Never average group averages directly unless group sizes are equal.

3-level practice ladder

Attempt all three before checking solutions

Foundation

Two groups in ratio 2:3 have averages 50 and 70. Find combined average.

CAT Standard

Men:women=3:2. Men's average salary is 20% higher than women's. Overall average is ₹33,000. Find women's average salary.

Advanced / Hybrid

Group A average is 60, group B average is 80, and combined average is 72. Find A:B group-size ratio.

PYQ Mapping

Verified mappingCAT 2023 · Slot 2

cat 2023 slot 2 shirt question uses average cost together with 25% markup and 10% discount.

Pattern Connections

#15 Percentage Distribution #19 Multiple Group Percentage Change #24 Percentage + Ratio
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Learning flow

  1. 1Recognition Cues
  2. 2How to Recognise
  3. 3Core Concept
  4. 4Formula
  5. 5Athena Shortcut
  6. 6Alternative Method
  7. 7Timed Drill
  8. 8Standard Example
  9. 9CAT-Level Example
  10. 10Common Trap
  11. 11Practice Ladder
  12. 12PYQ Mapping
  13. 13Connections
  14. 14Mastery

Attempt every example before opening its answer.