MINDMAPS FOR UPSCPET 2026 · VISUAL REVISION
Successive changes and a moving base
Track how each percentage step updates the base before the next operation begins
Successive Change Workflow
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Convert Rates to Multipliers
- Write a +p% rise as factor (1 + p/100) and a −q% fall as factor (1 − q/100).
- For example, +20% multiplies by 1.20 (or 6/5), while −20% multiplies by 0.80 (or 4/5).
- Fractional changes work identically: +1/6 multiplies by 7/6 and −1/6 multiplies by 5/6.
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Check Same-Base vs Sequential
- If two annual rates act on the same opening population, net them before compounding.
- With +2.5% growth and −0.5% migration on the same base, net yearly rate is 2.0%.
- If changes act one after another, multiply factors: 100 × 1.10 × 0.90 = 99 (net −1%).
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Compound Across Time Periods
- Two years at 2% net annual growth give multiplier 1.02² = 1.0404, or a 4.04% rise.
- Shortcut for two successive changes +a% and +b%: net % = a + b + (ab/100).
- The extra ab/100 term is the second-period change acting on the first period’s gain.
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Recompute the Updated Base
- When Morning (250) rises 20% to 300, Evening (320) exceeds it by 20/300 × 100 = 6 2/3%.
- Halving Store S returns (120 → 60) raises net retained (480 → 540) by 60/480 = 12.5%.
- With 500 of 1200 bus users, 300 new bus users give a share of 800/1500 = 53⅓%.
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