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Back to Percentage Blueprint
Pattern 29·Hybrid·L3

Percentage + Time, Speed & Distance

Very High FrequencyMust Master 90–120 sec

USE WHEN

Speed changes by a percentage and time/distance constraints must still hold.

BEST METHOD

Fixed Distance Inverse Method

TARGET

90–120 sec

MASTERY

not started

Recognition Cues

  • speed % changes
  • same distance or target average speed
  • time adjusts inversely

How to Recognise

Speed changes by a percentage and time/distance constraints must still hold.

Core Concept

For fixed distance, speed and time are inversely proportional.

D=ST;forfixedD,T2/T1=S1/S2.D=ST; for fixed D, T₂/T₁=S₁/S₂.D=ST;forfixedD,T2​/T1​=S1​/S2​.

Athena Shortcut

If speed rises x%, time falls by x/(100+x)×100%.

Alternative Method · Fixed Distance Inverse Method

Treat time as inversely proportional to speed for same-distance questions.

Timed drill

Identify the base or invariant before you calculate.

2:00

Attempt first · Standard Example

Speed rises 25%. Time for same distance changes by?

Attempt first · CAT-Level Example

40% of a journey is covered at 60 km/h. To average 50 km/h overall, find speed for remaining 60%.

Common Trap

  • Average speed is distance-weighted through time, not the arithmetic average of speeds.

3-level practice ladder

Attempt all three before checking solutions

Foundation

Speed falls 20%. For the same distance, by what percentage does travel time rise?

CAT Standard

40% of a 100 km journey is covered at 60 km/h. What speed is required for the remaining distance to average 50 km/h overall?

Advanced / Hybrid

Half a journey is covered at speed v and the other half at 1.2v. By what percentage is the average speed greater than v?

PYQ Mapping

Related archetypeCAT

This pattern is a recurring CAT arithmetic archetype.

Pattern Connections

#04 Percentage Increase / Decrease #07 Successive Percentage Changes #28 Percentage + Time & Work
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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.