Percentage calculations are very important for the Quantitative Aptitude section. Furthermore, questions about successive percentage changes appear every single year. You will often see these as population changes, consecutive discounts, or compound interest.
Instead of doing long math, you can use a simple algebra shortcut. This trick is called the Effective Percentage Formula. Let us learn how it works.
Understanding Successive Changes
First, what exactly is a successive change? A successive change happens when a value increases or decreases. After that, the second change applies directly to the new value. It does not apply to the original number.
For example, imagine a price increases by 20 percent and then decreases by 10 percent. The final result is not a simple 10 percent increase. Therefore, we need a better way to calculate this quickly.
The Master Shortcut Formula
For any two successive percentage changes (let us call them “a” and “b”), you can use this simple formula:
Net Change = [ a + b + (a x b / 100) ] %
However, you must remember these important sign rules:
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First, if the change is an Increase or Profit, use a positive (+) value.
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Second, if the change is a Decrease, Discount, or Loss, use a negative (-) value.
Real Exam Applications
Case 1: Two Consecutive Price Increases Question: The price of a book increases by 20% and later increases by 10%. What is the total net percentage increase?
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Here, a = +20 and b = +10.
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Now, apply the formula.
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Net Change = 20 + 10 + (20 x 10 / 100)
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Net Change = 30 + (200 / 100)
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Net Change = 30 + 2 = 32%
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Result: As a result, the price increased by a net total of 32%.
Case 2: One Increase and One Decrease Question: A town’s population increases by 30% in year one. However, it decreases by 20% in year two. Find the net percentage change.
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Here, a = +30 and b = -20.
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Next, apply the formula with the correct signs.
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Net Change = 30 + (-20) + (30 x -20 / 100)
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Net Change = 10 + (-600 / 100)
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Net Change = 10 – 6 = 4%
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Result: Because the answer is positive, the population saw a net 4% increase.
Quick Shortcut Rules to Memorize
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Two Increases (+10% and +10%): The net change is +21%. (Trick: 10 + 10 + 1)
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Two Increases (+20% and +20%): The net change is +44%. (Trick: 20 + 20 + 4)
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Same Increase & Decrease (+10% and -10%): This is always a 1% Loss.
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Same Increase & Decrease (+20% and -20%): This is always a 4% Loss.
In conclusion, mastering this single formula will save you precious time during the exam.