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Pattern 10·Core CAT·L2

Income × Expenditure × Savings

Very High FrequencyMust Master 60–90 sec

USE WHEN

Income, spending and savings percentages change and one original proportion is unknown.

BEST METHOD

Variable Equation Method

TARGET

60–90 sec

MASTERY

not started

Recognition Cues

  • income, expense, savings all linked
  • one percentage changes, one unknown share asked
  • savings treated as leftover

How to Recognise

Income, spending and savings percentages change and one original proportion is unknown.

Core Concept

Savings is the residual after expenditure: S = I − E.

I=E+S;applymultipliersseparatelytoIandE,thenequatenewsavings.I=E+S; apply multipliers separately to I and E, then equate new savings.I=E+S;applymultipliersseparatelytoIandE,thenequatenewsavings.

Athena Shortcut

Normalize original income to 100 or use variables I and E if percentages are asymmetric.

Alternative Method · Variable Equation Method

Let income = I and expenditure = E. Use S=I−E to build equations cleanly.

Timed drill

Identify the base or invariant before you calculate.

1:30

Attempt first · Standard Example

A person saves 20% of income. If income is ₹50,000, find expenditure.

Attempt first · CAT-Level Example

Income rises 20%, expenditure rises 10%, savings rise 50%. Find original expenditure as % of income.

Common Trap

  • A percentage change in savings cannot be applied directly to income or expenditure.

3-level practice ladder

Attempt all three before checking solutions

Foundation

A person earns ₹50,000 and saves 20% of income. Find expenditure.

CAT Standard

Income rises 20%, expenditure rises 10%, and savings rise 50%. Find original expenditure as a percentage of income.

Advanced / Hybrid

Income rises 25%, expenditure rises 20%, and savings rise 50%. Find original savings as a percentage of income.

PYQ Mapping

Verified mappingCAT 2024 · Slot 1

cat 2024 slot 1: income ratios, different rent shares, later income increases, fixed total rent.

Pattern Connections

#09 Price × Consumption × Expenditure #31 Percentage + Income + Ratio #32 Multi-Constraint CAT Percentage Problems
Sign in to save progressAll patterns

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.