All MindmapsSuggest a Topic Suggest a topic BilingualDefault language of all mindmaps
Blog
About

PET 2026 · CSAT

Choose the right percentage base

A four-step workflow to decode wording, fix the denominator and avoid base-shift traps

MINDMAPS FOR UPSCPET 2026 · VISUAL REVISION

Choose the right percentage base

A four-step workflow to decode wording, fix the denominator and avoid base-shift traps

Percentage Base Workflow
The percentage changes with the base180225+25%−20%The difference is 45 in both directions; the denominator changes.
The percentage changes with the baseSwipe sideways to explore the diagram.

  1. Decode the Question Phrase

    • ‘A is what % of B’ uses A/B × 100; ‘A exceeds B by what %’ uses (A − B)/B × 100.
    • Percentage change from initial value I to final value F is ((F − I)/I) × 100.
    • A percentage is meaningless until you name the reference quantity on which it acts.

  2. Fix the Reference Denominator

    • Name the reference quantity explicitly; place that value in the denominator.
    • Rising from 180 to 225 is 45/180 × 100 = 25%; reversing 225 to 180 is 45/225 × 100 = 20%.
    • Example: 82 exceeds 60 by (82 − 60)/60 × 100 ≈ 36.67%.

  3. Combine Groups and Invert Rates

    • For combined groups, sum numerators and denominators first: (480 + 720)/(600 + 900) = 80%.
    • For unequal groups, use group sizes as weights instead of an unweighted mean of rates.
    • If a known part equals r% of the whole, find the whole via Total = Part ÷ (r/100): 10 ÷ 0.40 = 25.

  4. Simplify First, Round Last

    • Cancel common factors before multiplying: 1890/2160 reduces to 7/8, giving 87.5%.
    • Keep exact fractions until the final step, then round: 80/310 × 100 = 800/31% ≈ 25.81%.
    • Distinguish percentage-point gap (60% − 50% = 10 points) from relative change (10/50 = 20%).
Understand · Connect · Recallmindmapsforupsc.com