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Successive Percentage Changes

Introduction

Sometimes, a value changes by a percentage more than once. For example: a price increases by 20% one year and decreases by 10% the next year. These are called successive percentage changes.

Direct addition or subtraction of percentages is not correct in these cases. We use a simple method to calculate the net effect.

Pattern: Successive Percentage Changes

Pattern

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

Net % = a + b + (a × b) / 100

If the result is positive → net increase, if negative → net decrease.

Step-by-Step Example

Question

A price is increased by 20% and then decreased by 10%. Find the net percentage change.

Solution

  1. Step 1: Write the given changes.

    First increase = +20%, Second change = -10%

  2. Step 2: Apply the formula.

    Net % = a + b + (a × b)/100
    = 20 + (-10) + (20 × -10)/100
    = 20 - 10 - 2
    = +8%

  3. Step 3: Interpret the result.

    Positive result means Net increase of 8%.

  4. Step 4: Quick Check with 100 method.

    Start with 100.
    After +20% → 120.
    After -10% → 120 - 12 = 108.
    Net = 108 - 100 = +8%. ✅

  5. Step 5: Final Answer.

    The net effect is an 8% increase.

Quick Variations

If both are increases: Eg: +10% and +20%. Net = 10 + 20 + (10×20)/100 = 32% increase.

If both are decreases: Eg: -10% and -20%. Net = -10 - 20 + (-10×-20)/100 = -28% (decrease).

If increase then decrease: Eg: +25%, -20%. Net = 25 - 20 - 5 = 0% (no change).

Trick to Always Use

  • Formula: Net % = a + b + (a×b)/100.
  • + value = increase, - value = decrease.
  • For quick check, assume initial value = 100 and apply changes step by step.
  • Always confirm by checking if the final is higher/lower than the original.

Summary

Summary

The Successive Percentage Change pattern calculates the combined effect of two or more percentage changes.

Net % = a + b + (a × b) / 100

  • Use positive for increase, negative for decrease.
  • If result > 0 → net increase.
  • If result < 0 → net decrease.
  • Cross-check using the 100 method.

Mastering this will save time and avoid mistakes in tricky exam questions.

Practice

(1/5)
1. A price is increased by 10% and then decreased by 10%. What is the net percentage change?
easy
A. 1% decrease
B. 0%
C. 2% decrease
D. 1% increase

Solution

  1. Step 1: State the successive changes

    Given changes: +10% and -10%.

  2. Step 2: Use the successive % formula

    Net % = a + b + (a×b)/100 = 10 + (-10) + (10×-10)/100 = 0 - 1 = -1% → 1% decrease.

  3. Final Answer:

    1% decrease → Option A

  4. Quick Check:

    Start 100 → after +10% = 110 → after -10% = 99 → net decrease = 1% ✅
Hint: Use Net% = a + b + (a×b)/100.
Common Mistakes: Assuming +10% and -10% cancel out to 0% without using the product term.
2. The salary of a person is increased by 20% and then again increased by 10%. Find the net percentage increase.
easy
A. 30%
B. 32%
C. 31%
D. 28%

Solution

  1. Step 1: State the successive increases

    Given changes: +20% and +10%.

  2. Step 2: Apply the formula

    Net % = 20 + 10 + (20×10)/100 = 30 + 2 = 32% increase.

  3. Final Answer:

    32% increase → Option B

  4. Quick Check:

    Start 100 → after +20% = 120 → after +10% = 132 → net increase = 32% ✅
Hint: Add the percentages and include (a×b)/100 term for successive increases.
Common Mistakes: Forgetting the (a×b)/100 term and giving 30% instead of 32%.
3. A shopkeeper increases the price of an item by 30% and then gives a discount of 20%. What is the net effect on price?
easy
A. 6% increase
B. 4% decrease
C. 2% increase
D. 4% increase

Solution

  1. Step 1: Identify successive change values

    Given changes: +30% and -20%.

  2. Step 2: Apply the net % formula

    Net % = 30 - 20 + (30×-20)/100 = 10 - 6 = 4% increase.

  3. Final Answer:

    4% increase → Option D

  4. Quick Check:

    Start 100 → after +30% = 130 → after -20% = 130 - 26 = 104 → net +4% ✅
Hint: Convert successive % to net using a + b + (a×b)/100; check with 100-method.
Common Mistakes: Ignoring the product term and reporting 10% instead of 4%.
4. A population decreases by 20% one year and increases by 25% the next year. What is the net percentage change?
medium
A. 5% increase
B. 0%
C. 2% decrease
D. 1% increase

Solution

  1. Step 1: Note the two changes

    Given changes: -20% and +25%.

  2. Step 2: Compute net % using formula

    Net % = -20 + 25 + (-20×25)/100 = 5 - 5 = 0% (no change).

  3. Final Answer:

    0% (no change) → Option B

  4. Quick Check:

    Start 100 → after -20% = 80 → after +25% = 100 → back to original ✅
Hint: Use the formula; many pairs cancel via the product term.
Common Mistakes: Adding -20 + 25 = 5% and assuming net +5% without the product term.
5. The price of sugar increased by 50% in one year and then decreased by 20% the next year. What is the net percentage change?
medium
A. 25% increase
B. 30% increase
C. 20% increase
D. 35% increase

Solution

  1. Step 1: State the successive changes

    Given changes: +50% and -20%.

  2. Step 2: Calculate net %

    Net % = 50 - 20 + (50×-20)/100 = 30 - 10 = 20% increase.

  3. Final Answer:

    20% increase → Option C

  4. Quick Check:

    Start 100 → after +50% = 150 → after -20% = 120 → net increase = 20% ✅
Hint: Compute net % using a + b + (a×b)/100 and keep track of signs.
Common Mistakes: Applying +50 - 20 = +30% incorrectly (misses -10% product correction).

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