Pattern 32·Hybrid·L3

Multi-Constraint CAT Percentage Problems

Very High FrequencyMust Master 90–120 sec

USE WHEN

A long word problem mixes percentages with ratios, averages, work, speed, composition or budgets and hides the main equation.

BEST METHOD

Invariant Mapping

TARGET

90–120 sec

MASTERY

not started

Recognition Cues

long mixed arithmetic story
multiple constraints together
need invariant + percentage model

How to Recognise

A long word problem mixes percentages with ratios, averages, work, speed, composition or budgets and hides the main equation.

Core Concept

Identify invariants and constraints first, normalize intelligently, then connect multipliers instead of solving every intermediate quantity.

No single formula: build from invariants such as I=E+S, D=ST, E=PQ, Work=Rate\times Time, weighted average, ratio conservation.

Athena Shortcut

Ask: What stays constant? What is the base of each percentage? Which quantities are multiplicative?

Alternative Method · Invariant Mapping

First identify what stays constant—budget, work, total, or distance—then write the percentage equation.

Timed drill

Identify the base or invariant before you calculate.

2:00

Attempt first · Standard Example

Income rises 20%, spending share rises from 50% to 55%. By what % does expenditure rise?

Attempt first · CAT-Level Example

Income rises 25%. Commodity allocation rises from 20% to 24% of income while commodity price rises 50%. Find consumption change.

Common Trap

Long wording is often camouflage. Reduce the question to 1–2 invariant equations.

3-level practice ladder

Attempt all three before checking solutions

Foundation

Income rises 20%, spending share rises from 40% to 45%, and commodity price rises 35%. Find change in quantity consumed.

CAT Standard

A business has divisions A and B in original revenue ratio 3:2. A revenue rises 20% while B falls 10%. If total original revenue was ₹50 lakh, find new total revenue.

Advanced / Hybrid

Income rises 25%. The share spent on a commodity rises from 20% to 24% of income while its price rises 50%. Find change in quantity consumed.

PYQ Mapping

Verified mappingCAT 2023 · Slot 3

cat 2023 slot 3 fruit-stock percentage constraints and cat 2024 slot 3 boys/girls activity percentages are strong multi-constraint examples.

Pattern Connections

#09 Price × Consumption × Expenditure #10 Income × Expenditure × Savings #23 Percentage Equations

Core Concept

Identify invariants and constraints first, normalize intelligently, then connect multipliers instead of solving every intermediate quantity.

No single formula: build from invariants such as I=E+S, D=ST, E=PQ, Work=Rate\times Time, weighted average, ratio conservation.

Attempt all three before checking solutions

Foundation

Income rises 20%, spending share rises from 40% to 45%, and commodity price rises 35%. Find change in quantity consumed.

CAT Standard

A business has divisions A and B in original revenue ratio 3:2. A revenue rises 20% while B falls 10%. If total original revenue was ₹50 lakh, find new total revenue.

Advanced / Hybrid