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Pattern 12·Core CAT·L2

Appreciation / Depreciation

Medium FrequencyImportant 60–90 sec

USE WHEN

Value of asset/machine/property changes repeatedly by a percentage.

BEST METHOD

Factor Cancellation

TARGET

60–90 sec

MASTERY

not started

Recognition Cues

  • asset value, machine, property
  • appreciation/depreciation yearly
  • repeated valuation

How to Recognise

Value of asset/machine/property changes repeatedly by a percentage.

Core Concept

Appreciation and depreciation are compound change problems.

Vn=V0(1±r/100)nVₙ=V₀(1±r/100)ⁿVn​=V0​(1±r/100)n

Athena Shortcut

For varying annual rates, multiply annual factors instead of using a single-power formula.

Alternative Method · Factor Cancellation

Spot when appreciation and depreciation factors cancel, e.g., 0.8 × 1.25 = 1.

Timed drill

Identify the base or invariant before you calculate.

1:30

Attempt first · Standard Example

A machine worth ₹5 lakh depreciates 10% in a year. New value?

Attempt first · CAT-Level Example

An asset depreciates 20% in year 1 and appreciates 25% in year 2. Net change?

Common Trap

  • Equal-looking percentage rates may exactly offset only when their multipliers are reciprocal.

3-level practice ladder

Attempt all three before checking solutions

Foundation

A car depreciates 10% annually for two years. Find total percentage depreciation.

CAT Standard

An asset appreciates 25% and then depreciates 20%. Find net change.

Advanced / Hybrid

A vehicle worth ₹8,00,000 depreciates 15% in year 1 and 10% in year 2. Find its value after two years.

PYQ Mapping

Verified mappingCAT 2021 · Slot 2

cat 2021 slot 2: investment loses a percentage in year 1 and grows by a related percentage in year 2.

Pattern Connections

#07 Successive Percentage Changes #11 Population Growth / Decline #30 Percentage + SI / CI
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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.