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Back to Percentage Blueprint
Pattern 28·Hybrid·L3

Percentage + Time & Work

Very High FrequencyMust Master 90–120 sec

USE WHEN

Worker efficiency changes by a percentage, or workforce changes during the job.

BEST METHOD

LCM Work Method

TARGET

90–120 sec

MASTERY

not started

Recognition Cues

  • efficiency % changes
  • time/work relationship
  • join/leave workers

How to Recognise

Worker efficiency changes by a percentage, or workforce changes during the job.

Core Concept

Work rate is proportional to efficiency; time is inversely proportional to efficiency for fixed work.

Work=Rate×Time;ifefficiencyrisesx%,timemultiplier=1/(1+x/100).Work = Rate\times Time; if efficiency rises x\%, time multiplier = 1/(1+x/100).Work=Rate×Time;ifefficiencyrisesx%,timemultiplier=1/(1+x/100).

Athena Shortcut

Use efficiency units and LCM total work.

Alternative Method · LCM Work Method

Take total work as an LCM-based unit model and adjust rates after % changes.

Timed drill

Identify the base or invariant before you calculate.

2:00

Attempt first · Standard Example

A worker becomes 25% more efficient. By what % does time fall for same work?

Attempt first · CAT-Level Example

A:B efficiency=3:2. Together they finish in 12 days. After 4 days, A's efficiency falls 25%. Extra time?

Common Trap

  • A 25% efficiency increase does not mean a 25% time decrease.

3-level practice ladder

Attempt all three before checking solutions

Foundation

Efficiency falls 20%. By what percentage does time rise for the same work?

CAT Standard

Efficiency rises 50%. By what percentage does time fall for the same work?

Advanced / Hybrid

A:B efficiency=3:2 and together they finish a job in 12 days. After 4 days, A's efficiency falls 25%. Find total completion time.

PYQ Mapping

Related archetypeCAT

This pattern is a recurring CAT arithmetic archetype.

Pattern Connections

#09 Price × Consumption × Expenditure #24 Percentage + Ratio #29 Percentage + Time, Speed & Distance
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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.