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Back to Percentage Blueprint
Pattern 26·Hybrid·L3

Percentage + Profit / Loss

Very High FrequencyMust Master 90–120 sec

USE WHEN

Different items have different profit/loss percentages and cost weights, or markup/discount chains appear.

BEST METHOD

Cost-Weight Method

TARGET

90–120 sec

MASTERY

not started

Recognition Cues

  • profit/loss % with different weights
  • markup-discount chain
  • overall result needed

How to Recognise

Different items have different profit/loss percentages and cost weights, or markup/discount chains appear.

Core Concept

Overall profit/loss is based on total cost, not average of individual percentages.

OverallP/L%=(ΣSP−ΣCP)/ΣCP×100Overall P/L\% = (ΣSP−ΣCP)/ΣCP \times 100OverallP/L%=(ΣSP−ΣCP)/ΣCP×100

Athena Shortcut

When CP ratio is known, use ratio units as cost weights.

Alternative Method · Cost-Weight Method

Take cost ratio as actual cost units and compute total SP and total CP.

Timed drill

Identify the base or invariant before you calculate.

2:00

Attempt first · Standard Example

Items cost in ratio 2:3. First gains 20%, second loses 10%. Overall result?

Attempt first · CAT-Level Example

A trader marks 60% above CP and gives successive discounts 20% and 10%. Profit%?

Common Trap

  • Profit percentages cannot be averaged without weighting by their cost bases.

3-level practice ladder

Attempt all three before checking solutions

Foundation

Two items have cost prices in ratio 1:2. The first gains 30% and the second loses 10%. Find overall result.

CAT Standard

Two articles are sold at the same selling price. One gives 20% profit and the other 20% loss. Find overall result.

Advanced / Hybrid

An item is marked 50% above cost and sold at 20% discount. Find profit percentage.

PYQ Mapping

Verified mappingCAT 2023 · Slot 1

cat 2023 slot 1: same selling price with 20% profit and 10% loss. multiple 2024–2025 cat questions also mix markup, discount and profit.

Pattern Connections

#07 Successive Percentage Changes #22 Repeated Percentage Operations #24 Percentage + Ratio
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Learning flow

  1. 1Recognition Cues
  2. 2How to Recognise
  3. 3Core Concept
  4. 4Formula
  5. 5Athena Shortcut
  6. 6Alternative Method
  7. 7Timed Drill
  8. 8Standard Example
  9. 9CAT-Level Example
  10. 10Common Trap
  11. 11Practice Ladder
  12. 12PYQ Mapping
  13. 13Connections
  14. 14Mastery

Attempt every example before opening its answer.