Successive Percentage Change and Applications

Successive change formula

When a value changes by a% and then by b%, the net change is:

Net % = a + b + (a × b)/100

Use a minus sign for a decrease.

Examples

• +20% then +10%: 20 + 10 + 200/100 = +32%.
• +10% then −10%: 10 − 10 − 100/100 = −1% (a net loss, not zero!).
• −20% then −20%: −20 − 20 + 400/100 = −36%.

Multiplier method

Convert each change into a multiplier: +20% → 1.2, −15% → 0.85. Multiply them: 1.2 × 0.85 = 1.02 → +2%.

Applications (RRB NTPC)

1. Population growth: P × (1 + r/100)ⁿ.
2. Price–consumption: if price rises by r%, consumption must fall by r/(100 + r) × 100% to keep expenditure same. Price +25% → cut consumption by 20%.
3. Salary: raise of 10% then cut of 10% leaves salary 1% lower.
4. Area: if length and breadth both rise 10%, area rises 21%.

Analogy

Successive percentages are like climbing and sliding on a moving staircase. Go up 10% of your height, then slide down 10% — but the second 10% is taken from your new, higher position, so you slide further than you climbed and end up 1% lower than where you started.