Percentages • Topic 2 of 5

Percentage Change

Percentage change always uses the ORIGINAL value as the base: change% = (new − old)/old × 100. The classic CAT trap is the asymmetry of increase and decrease. If a price rises 25% and then falls 25%, you do NOT get back to the start — you end lower, because the second 25% is taken on a larger number. A clean way to handle "A is x% more/less than B" is the multiplier view: +x% means ×(1+x/100), −x% means ×(1−x/100). Also master the inverse phrasing: if A is 25% more than B, then B is only 20% less than A, because the base changed from B to A. The shortcut is B is [x/(100±x)]×100% — memorise the common pairs (¼↔⅕, ⅓↔¼, ½↔⅓).

✅ Solved examples

1. A salary rises from ₹40,000 to ₹46,000. Find the percentage increase.
Change = 6000 on a base of 40000. (6000/40000) × 100 = 15%.
2. A number is increased by 25% then decreased by 20%. Net change?
Multiplier = 1.25 × 0.80 = 1.00 ⇒ 0% net change. (The classic "they cancel" pair.)
3. If A is 40% more than B, by what percent is B less than A?
B is [40/(100+40)]×100 = 4000/140 ≈ 28.57% less than A.
4. A’s income is 25% more than B’s. B’s is 20% more than C’s. A is what % more than C?
A = 1.25B, B = 1.20C ⇒ A = 1.25×1.20 C = 1.5C ⇒ 50% more.

✏️ Practice — try these, take hints as needed

1. A quantity rises from 80 to 100. Percentage increase?
Base is 80.
Change = 20.
(20/80)×100.
25%
2. A price falls from 100 to 80. Percentage decrease?
Base is 100.
Change = 20.
(20/100)×100.
20% (note: not 25%)
3. Increase 50 by 30% then decrease the result by 30%. Final value?
×1.3 then ×0.7.
50 × 0.91.
Net multiplier 0.91.
45.5
4. If A is 20% less than B, by what percent is B more than A?
Use x/(100−x).
20/(100−20).
20/80 × 100.
25%
5. X is 25% more than Y, Y is 25% less than Z. X is what % of Z?
X = 1.25Y, Y = 0.75Z.
X = 1.25 × 0.75 Z.
= 0.9375Z.
93.75%

📝 Topic test — 8 questions

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