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Back to Percentage Blueprint
Pattern 02·Foundation·L1

Percentage of a Quantity

High FrequencyMust Master 45–60 sec

USE WHEN

A direct part of a total is requested: x% of N.

BEST METHOD

Fraction Conversion Method

TARGET

45–60 sec

MASTERY

not started

Recognition Cues

  • 'x% of' a number
  • part of total directly asked
  • original total known

How to Recognise

A direct part of a total is requested: x% of N.

Core Concept

Convert the percentage into a multiplier and apply it to the base quantity.

x%ofN=(x/100)Nx\% of N = (x/100)Nx%ofN=(x/100)N

Athena Shortcut

Use fraction equivalents where possible: 12.5%=1/8, 16.67%≈1/6, 25%=1/4, 33.33%≈1/3, 37.5%=3/8, 62.5%=5/8.

Alternative Method · Fraction Conversion Method

Convert awkward percentages into fractions first, then multiply instead of using decimals.

Timed drill

Identify the base or invariant before you calculate.

1:00

Attempt first · Standard Example

Find 17.5% of 480.

Attempt first · CAT-Level Example

A company spends 35% of its revenue on salaries. Of the remaining revenue, 20% is spent on marketing. What percentage of revenue remains after both expenses?

Common Trap

  • ‘20% of the remaining’ is not 20% of the original total.

3-level practice ladder

Attempt all three before checking solutions

Foundation

35% of a number is 126. Find 15% of the same number.

CAT Standard

12.5% of a number is 45. Find 37.5% of that number.

Advanced / Hybrid

45% of students choose Course A. Of the remaining students, 20% choose Course B. What percentage choose either A or B?

PYQ Mapping

Related archetypeCAT

direct percentage-of-total operations recur inside distribution, investment and profit questions; no exact standalone mapping asserted.

Pattern Connections

#03 A as a Percentage of B #04 Percentage Increase / Decrease #05 Reverse Percentage
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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.