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Back to Percentage Blueprint
Pattern 07·Core CAT·L2

Successive Percentage Changes

High FrequencyMust Master 60–90 sec

USE WHEN

A quantity undergoes two or more percentage changes one after another.

BEST METHOD

Multiplier Chain

TARGET

60–90 sec

MASTERY

not started

Recognition Cues

  • two or more successive changes
  • year by year changes
  • markup + discount / rise + fall

How to Recognise

A quantity undergoes two or more percentage changes one after another.

Core Concept

Each change acts on the updated value, so multiply change factors.

Netfora%,b%=a+b+(ab/100),takingdecreasesasnegative.Net for a\%, b\% = a+b+(ab/100), taking decreases as negative.Netfora%,b%=a+b+(ab/100),takingdecreasesasnegative.

Athena Shortcut

Multiplier method is safer: final/original = ∏(1±r/100).

Alternative Method · Multiplier Chain

Write 1.20 × 0.90 × 1.10 rather than using the net-percent formula repeatedly.

Timed drill

Identify the base or invariant before you calculate.

1:30

Attempt first · Standard Example

A price rises 20% and then falls 10%. Find net change.

Attempt first · CAT-Level Example

A population rises 20%, falls 25%, then rises 10%. Find net change.

Common Trap

  • Never simply add percentage changes unless all act on the same base.

3-level practice ladder

Attempt all three before checking solutions

Foundation

A value rises 25% and then rises 20%. Find the net increase.

CAT Standard

A price rises 30% and then falls 20%. Find the net change.

Advanced / Hybrid

A quantity rises 20%, then 10%, then falls 25%. Find the net change.

PYQ Mapping

Verified mappingCAT 2024 · Slot 3

cat 2024 slot 3: two successive salary increments, with the second percentage twice the first.

Pattern Connections

#08 Returning to Original Value #11 Population Growth / Decline #22 Repeated Percentage Operations
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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.