Successive Percentage Change: Formulas, Rules and Examples

Successive Percentage Change calculates the overall effect of two or more percentage changes applied one after another. The second percentage is applied to the changed value, not the original value. Use signed changes in the formula net change = a + b + ab/100, or multiply the corresponding factors for several changes.

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What Is Successive Percentage Change?

Successive percentage change is the combined effect of percentage changes applied consecutively to the same quantity. The base for each new change is the value obtained after the previous change.

For two successive changes of a% and b%, where increases are positive and decreases are negative, the net percentage change is a + b + ab/100. For example, increases of 20% and 10% give 20 + 10 + (20 × 10)/100 = 32%, not 30%, because the second increase is calculated on the increased value.

Successive Percentage Change Formula & Tricks

Important Formulas

Two successive percentage changes
Net percentage change = a + b + (ab/100)

Use positive values for increases and negative values for decreases.

Successive multiplier method
Final value = Original value × (1 + a/100) × (1 + b/100)

Replace a decrease by a negative percentage, so a decrease of b% uses (1 − b/100).

Three or more changes
Final value = Original value × ∏(1 + rᵢ/100)

Multiply the factor for every change, using positive rates for increases and negative rates for decreases.

Successive discounts
Equivalent discount = d₁ + d₂ − (d₁d₂/100)

This formula gives the single discount equivalent to discounts of d₁% and d₂% applied successively.

Reverse percentage calculation
Original value = Final value ÷ (1 + r/100)

Use r as positive for an increase and negative for a decrease. For a decrease of d%, the divisor is 1 − d/100.

Quick Tricks

Use signed percentages

Treat an increase as positive and a decrease as negative. This allows the same formula to handle all combinations of changes.

Example: A 25% increase followed by a 20% decrease gives 25 − 20 + (25 × −20)/100 = 0%.
Equal increase and decrease

An increase of x% followed by a decrease of x% always produces a loss of x²/100%.

Example: A 10% increase followed by a 10% decrease gives a net change of −10²/100 = −1%.
Multiply factors for many changes

For three or more changes, multiplying factors is safer than repeatedly applying the two-change formula.

Example: For increases of 10%, 20% and 25%, the factor is 1.10 × 1.20 × 1.25 = 1.65, so the net increase is 65%.

Successive Percentage Change Concepts

Two Successive Increases

Two successive increases of a% and b% produce a net increase of a + b + ab/100%.

The product term ab/100 represents the increase on the amount added by the first percentage. For example, a value of 500 increased by 10% and then 20% becomes 500 × 1.10 × 1.20 = 660, giving a net increase of 32%.

Example: For 15% and 10% increases: net increase = 15 + 10 + (15 × 10)/100 = 26.5%.

Increase Followed by Decrease

An increase of a% followed by a decrease of b% gives a net change of a − b − ab/100%.

The decrease is calculated on the value after the increase. For an original value of 1,000 with a 20% increase followed by a 10% decrease, the final value is 1,000 × 1.20 × 0.90 = 1,080, so the net increase is 8%.

Example: For a 30% increase and a 20% decrease: net change = 30 − 20 − 6 = 4% increase.

Two Successive Decreases

Two successive decreases of a% and b% produce a net decrease of a + b − ab/100%.

The second decrease is taken from the already reduced value. Thus, two discounts of 20% and 10% are equivalent to a discount of 20 + 10 − 2 = 28%, not 30%.

Example: A price of ₹2,000 after successive decreases of 20% and 10% becomes ₹2,000 × 0.80 × 0.90 = ₹1,440.

Reverse Successive Percentage Change

To find an original value from a final value, divide by the combined multiplier rather than subtracting the percentage from the final value.

If a quantity increases by 25% and becomes 500, its original value is 500 ÷ 1.25 = 400. If it decreases by 20% and becomes 640, its original value is 640 ÷ 0.80 = 800.

Example: After successive increases of 10% and 20%, a value is 660. Original value = 660 ÷ (1.10 × 1.20) = 500.

Successive Percentage Change Video Lessons

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Successive Percentage Change Formula

Learn the combined formula for calculating successive percentage changes and understand how multiple increases or decreases affect the final value.

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Practice Successive Percentage Change Questions

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1Ricky purchased a shirt for $2000. The discount offered for the shirt is 10%. Find how many dollars has he given to the cashier?→ 2If an item marked at ₹3,392 is sold for ₹1,696, then what is the discount percentage?→ 3Two numbers have HCF 12, LCM 480, and their sum is 156. Find the numbers.→ 4An article is marked for ₹2,000. A 25% discount is offered on the marked price, followed by a second discount of 10% on the new price. What is the final selling price of the article?→ 5Total cost price of 880 articles is Rs. 400. Total selling price of 11 articles is Rs. 7. What is the profit percentage? (Cost price of all the articles is same. Selling price of all the articles is same.)→ 6Article M is sold at a reduction of ₹3,000 from its original price, and Article N is sold at a reduction of ₹2,500 from its original price. If the original prices of both articles were ₹10,000, reduction in price of M is R1% and reduction in price of N is R2%, find the difference between R1 and R2.→ 7An online seller purchases a laptop at ₹40,000. He lists it at a 25% markup. Due to a festive sale, he gives a flat 10% discount on the listed price and offers free shipping costing him ₹500. What is the net profit or loss percentage?→ 8How many numbers between 351 and 650 are divisible by 7?→ 9The largest four-digit number which when divided by 12, 8 and 11 leaves the remainder 3 in each case, is:→ 10The least value of x, so that the number 73318x4 is divisible by 8 is→

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Quick Revision Notes

Successive Percentage Change Revision Points

Use signed percentages or successive multipliers to calculate the final value and net change.

  • For two changes, net percentage change = a + b + ab/100.
  • Use positive signs for increases and negative signs for decreases.
  • For several changes, final value = original value × product of all percentage factors.
  • An increase of x% followed by a decrease of x% causes a loss of x²/100%.
  • Two successive discounts d₁% and d₂% equal one discount of d₁ + d₂ − d₁d₂/100%.
  • To find the original value, divide the final value by the combined multiplier.

Successive Percentage Change FAQs

What is the formula for two successive percentage changes?

The formula is net percentage change = a + b + ab/100, where increases are positive and decreases are negative.

What is the net change for a 20% increase followed by a 10% decrease?

Net change = 20 − 10 − (20 × 10)/100 = 8% increase.

Are two successive increases of 10% and 20% equal to a 30% increase?

No. The net increase is 10 + 20 + 2 = 32%, because the 20% increase is applied after the first increase.

What is the equivalent discount for successive discounts of 15% and 20%?

Equivalent discount = 15 + 20 − (15 × 20)/100 = 32%.

What happens when a value increases and then decreases by the same percentage?

It results in a loss, not no change. Equal successive changes of x% cause a net loss of x²/100%; for 20%, the loss is 4%.

How do you find the original value after a 25% increase?

Divide the final value by 1.25. For example, if the final value is 750, the original value is 750 ÷ 1.25 = 600.

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