Pattern 27·Hybrid·L3

Percentage + Mixture

High FrequencyMust Master 90–120 sec

USE WHEN

Concentration percentages combine with addition/removal/replacement.

BEST METHOD

Alligation / Component Method

TARGET

90–120 sec

MASTERY

not started

Recognition Cues

solution/milk-water concentration
final concentration asked
mix/add/remove component

How to Recognise

Concentration percentages combine with addition/removal/replacement.

Core Concept

Treat percentage concentration as component quantity / total quantity.

Component = concentration\times volume; final concentration = total component/final volume.

Athena Shortcut

Use alligation for direct mixing; use component accounting for addition/removal.

Alternative Method · Alligation / Component Method

Use alligation for direct mixing and component accounting for addition/removal.

Timed drill

Identify the base or invariant before you calculate.

2:00

Attempt first · Standard Example

20 L of 30% solution mixed with 30 L of 50% solution. Final concentration?

Attempt first · CAT-Level Example

A 50 L mixture is 40% milk. 10 L water is added. New milk percentage?

Common Trap

Adding water changes total volume but not the amount of original solute/component.

3-level practice ladder

Attempt all three before checking solutions

Foundation

30 L of 20% solution is mixed with 20 L of 50% solution. Find final concentration.

CAT Standard

40 L of 25% solution is mixed with 60 L of 55% solution. Find final concentration.

Advanced / Hybrid

A 50 L mixture contains 40% milk. 10 L water is added. Find new milk percentage.

PYQ Mapping

Verified mappingCAT 2022 · Slot 1

cat 2022 slot 1: syrup and juice with different costs, profit percentages, mixing and overall profit.

Pattern Connections

#15 Percentage Distribution #20 Replacement & Composition #25 Percentage + Average

Core Concept

Treat percentage concentration as component quantity / total quantity.

Component = concentration\times volume; final concentration = total component/final volume.

Attempt all three before checking solutions

Foundation

30 L of 20% solution is mixed with 20 L of 50% solution. Find final concentration.

CAT Standard

40 L of 25% solution is mixed with 60 L of 55% solution. Find final concentration.

Advanced / Hybrid