Pattern 24·Hybrid·L3

Percentage + Ratio

Very High FrequencyMust Master 90–120 sec

USE WHEN

Quantities are in a ratio, then one or more components change by percentages.

BEST METHOD

Ratio Units Method

TARGET

90–120 sec

MASTERY

not started

Recognition Cues

ratio first, then % change
new ratio/total share asked
mixed ratio-percentage transformation

How to Recognise

Quantities are in a ratio, then one or more components change by percentages.

Core Concept

Represent ratio terms as convenient base units, apply percentage multipliers, then simplify.

If A:B=m:n, after changes a\%,b\% → A':B'=m(1+a):n(1+b) in decimal multipliers.

Athena Shortcut

Do not calculate absolute values unless total is required.

Alternative Method · Ratio Units Method

Take ratio terms as 2x, 3x etc. and apply percentage changes before simplifying.

Timed drill

Identify the base or invariant before you calculate.

2:00

Attempt first · Standard Example

A:B=2:3. A rises 50%, B falls 20%. New ratio?

Attempt first · CAT-Level Example

Men:women=3:2. Men rise 20%, women rise 50%. What % of new total are women?

Common Trap

Apply percentage change to each ratio component before recombining.

3-level practice ladder

Attempt all three before checking solutions

Foundation

A:B=4:5. A decreases 25% and B increases 20%. Find the new ratio.

CAT Standard

Men:women=3:2. Men increase 20% and women increase 50%. What percentage of the new total are women?

Advanced / Hybrid

A:B:C=2:3:5. A rises 50%, B falls 20%, C rises 10%. Find the new ratio.

PYQ Mapping

Verified mappingCAT 2025 · Slot 2

cat 2025 slot 2 amount division mixes percentages and ratios. cat 2024 slot 1 mixes income ratios with percentage contributions.

Pattern Connections

#06 More Than / Less Than #17 Changing Percentage Base #31 Percentage + Income + Ratio

Core Concept

Represent ratio terms as convenient base units, apply percentage multipliers, then simplify.

If A:B=m:n, after changes a\%,b\% → A':B'=m(1+a):n(1+b) in decimal multipliers.

Attempt all three before checking solutions

Foundation

A:B=4:5. A decreases 25% and B increases 20%. Find the new ratio.

CAT Standard

Men:women=3:2. Men increase 20% and women increase 50%. What percentage of the new total are women?

Advanced / Hybrid