Pattern 31·Hybrid·L3

Percentage + Income + Ratio

High FrequencyMust Master 90–120 sec

USE WHEN

Two or more people/groups have incomes/expenditures in a ratio and percentage changes alter the ratio.

BEST METHOD

Ratio × Savings Share Method

TARGET

90–120 sec

MASTERY

not started

Recognition Cues

income ratio + savings/spending %
new ratio of savings or incomes
allocation share changes

How to Recognise

Two or more people/groups have incomes/expenditures in a ratio and percentage changes alter the ratio.

Core Concept

Convert ratio units into algebraic bases, then apply the percentage multipliers.

If I₁:I₂=m:n, new ratio=m(1+a):n(1+b).

Athena Shortcut

Keep ratio units symbolic unless a total/absolute amount is required.

Alternative Method · Ratio × Savings Share Method

Compute savings units directly from income ratio and savings percentages.

Timed drill

Identify the base or invariant before you calculate.

2:00

Attempt first · Standard Example

A:B incomes=4:5. A rises 25%, B rises 20%. New ratio?

Attempt first · CAT-Level Example

A:B incomes=3:4. A spends 80% and B spends 75% of income. Find ratio of their savings.

Common Trap

Income ratio does not automatically equal expenditure or savings ratio.

3-level practice ladder

Attempt all three before checking solutions

Foundation

Income ratio A:B=2:3. A saves 25% and B saves 20%. Find savings ratio.

CAT Standard

Income ratio A:B=3:4. A spends 80% and B spends 75%. Find savings ratio.

Advanced / Hybrid

Three incomes are in ratio 6:5:4. They contribute 10%, 12% and 15% respectively toward a fixed common expense. Next month incomes rise 20%, 10% and 25%, while the expense is unchanged. What percentage of their new total income is the expense?

PYQ Mapping

Verified mappingCAT 2024 · Slot 1

cat 2024 slot 1: incomes in ratio 8:6:5, different rent percentages, later income increases with fixed rent.

Pattern Connections

#10 Income × Expenditure × Savings #24 Percentage + Ratio #23 Percentage Equations

Attempt all three before checking solutions

Foundation

Income ratio A:B=2:3. A saves 25% and B saves 20%. Find savings ratio.

CAT Standard

Income ratio A:B=3:4. A spends 80% and B spends 75%. Find savings ratio.

Advanced / Hybrid

Three incomes are in ratio 6:5:4. They contribute 10%, 12% and 15% respectively toward a fixed common expense. Next month incomes rise 20%, 10% and 25%, while the expense is unchanged. What percentage of their new total income is the expense?