Pattern 23·Advanced·L3

Percentage Equations

Very High FrequencyMust Master 90–120 sec

USE WHEN

A word problem gives several percentage relationships but no actual base values.

BEST METHOD

Normalization Method

TARGET

90–120 sec

MASTERY

not started

Recognition Cues

wordy condition-based percent equations
actual values not given
need algebra/normalization

How to Recognise

A word problem gives several percentage relationships but no actual base values.

Core Concept

Translate each statement into an algebraic equation; normalize only when it reduces unknowns.

Use variables + multiplier equations; solve ratios first before absolute values.

Athena Shortcut

When only a ratio is required, set one variable to 100 instead of solving fully.

Alternative Method · Normalization Method

Assume one variable as 100 when only a ratio or relative comparison is needed.

Timed drill

Identify the base or invariant before you calculate.

2:00

Attempt first · Standard Example

A is 30% of B and B is 40% of C. A is what % of C?

Attempt first · CAT-Level Example

A's income is 25% above B's. A saves 20% of income and B saves 30% of income. If their savings are equal, find ratio of their incomes.

Common Trap

Long wordings often hide simple percentage equations. Translate sentence by sentence.

3-level practice ladder

Attempt all three before checking solutions

Foundation

A is 40% of B, and B is 150% of C. A is what percentage of C?

CAT Standard

A is 25% more than B, while B is 20% less than C. Compare A and C.

Advanced / Hybrid

A saves 20% of income and B saves 30%. If their savings are equal, find the ratio of their incomes A:B.

PYQ Mapping

Verified mappingCAT 2025 · Slot 1

cat 2025 slot 1 investment split across stocks, bonds and gold converts percentage relations into equations.

Pattern Connections

#17 Changing Percentage Base #31 Percentage + Income + Ratio #32 Multi-Constraint CAT Percentage Problems

Core Concept

Translate each statement into an algebraic equation; normalize only when it reduces unknowns.

Use variables + multiplier equations; solve ratios first before absolute values.

Attempt all three before checking solutions

Foundation

A is 40% of B, and B is 150% of C. A is what percentage of C?

CAT Standard

A is 25% more than B, while B is 20% less than C. Compare A and C.

Advanced / Hybrid