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Back to Percentage Blueprint
Pattern 05·Foundation·L1

Reverse Percentage

High FrequencyMust Master 45–60 sec

USE WHEN

Final value is known after a percentage increase/decrease; original value is asked.

BEST METHOD

Equation Method

TARGET

45–60 sec

MASTERY

not started

Recognition Cues

  • final value known after % change
  • original/base value asked
  • discount/increase reversed

How to Recognise

Final value is known after a percentage increase/decrease; original value is asked.

Core Concept

Undo the multiplier instead of subtracting the percentage from the final value.

Original=Final/(1±x/100)Original = Final/(1±x/100)Original=Final/(1±x/100)

Athena Shortcut

After +25%, divide by 1.25; after −20%, divide by 0.80.

Alternative Method · Equation Method

Let original = x, build x(1±r/100)=final, then solve directly.

Timed drill

Identify the base or invariant before you calculate.

1:00

Attempt first · Standard Example

After a 25% increase, salary is ₹75,000. Find original salary.

Attempt first · CAT-Level Example

After successive discounts of 20% and 10%, an item sells for ₹1,440. Find marked price.

Common Trap

  • Do not add back 30%; successive discounts are multiplicative.

3-level practice ladder

Attempt all three before checking solutions

Foundation

After a 15% decrease, a value becomes 340. Find the original value.

CAT Standard

After a 15% increase, a salary becomes ₹1,380. Find the original salary.

Advanced / Hybrid

An item sells for ₹1,440 after successive discounts of 20% and 10%. Find the marked price.

PYQ Mapping

Related archetypeCAT

reverse percentage appears inside marked-price, discount and profit questions; exact standalone mapping not asserted.

Pattern Connections

#07 Successive Percentage Changes #08 Returning to Original Value #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.