Comparison of Percentages: Formulas, Rules and Examples

Comparison of Percentages involves finding how two percentages or quantities differ from each other. The comparison may be expressed as a difference in percentage points, a ratio, or a percentage increase or decrease. The correct denominator is the original or reference value used for comparison.

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What Is Comparison of Percentages?

Comparison of percentages means measuring the difference or relative change between two percentage values or quantities. It can be written as a percentage-point difference or as a percentage increase or decrease.

For two values A and B, the absolute difference is A − B. If B is the reference value, the percentage by which A exceeds B is ((A − B) ÷ B) × 100. When comparing percentage values p% and q%, their difference in percentage points is p − q, while their relative comparison is ((p − q) ÷ q) × 100 if q is the reference.

Comparison of Percentages Formula & Tricks

Important Formulas

Percentage increase over a reference value
Percentage increase = [(A − B) ÷ B] × 100

B is the original or reference value, and A is the new or compared value.

Percentage decrease from a reference value
Percentage decrease = [(A − B) ÷ A] × 100

When A is the original value and B is the smaller new value, divide the decrease by A.

Difference between two percentages
Difference in percentage points = p − q

Subtract the smaller percentage from the larger percentage. Do not divide by the reference percentage.

Relative comparison of two percentages
Relative difference = [(p − q) ÷ q] × 100

This gives how much p% is greater than q%, with q% as the reference percentage.

Quick Tricks

Fix the denominator first

The denominator must be the value against which the comparison is made. A is greater than B by a different percentage than B is less than A.

Example: If A = 120 and B = 100, A is 20% greater than B because 20 ÷ 100 × 100 = 20%. B is 16.67% less than A because 20 ÷ 120 × 100 = 16.67%.
Separate percentage points from percent change

Subtracting two percentages gives percentage points. Dividing the difference by the original percentage gives relative percentage change.

Example: The change from 40% to 50% is 10 percentage points, but the relative increase is (10 ÷ 40) × 100 = 25%.
Use a ratio for direct comparison

The ratio p:q compares two percentage values without converting them into decimals. It can be simplified like any ordinary ratio.

Example: The ratio of 24% to 18% is 24:18 = 4:3.

Comparison of Percentages Concepts

Comparing Two Quantities

To find how much A is greater than B in percentage terms, divide their difference by B and multiply by 100.

The formula is [(A − B) ÷ B] × 100, where B is the reference quantity. If A < B, the result is negative when the signed formula is used, indicating a decrease from B to A.

Example: For A = 75 and B = 60, the increase is [(75 − 60) ÷ 60] × 100 = 25%.

Percentage Points and Relative Percentage Change

The difference between p% and q% is p − q percentage points, whereas the relative change uses q as the denominator.

These two measures are not interchangeable. From 30% to 36%, the difference is 6 percentage points, while the relative increase is (6 ÷ 30) × 100 = 20%.

Example: A pass rate rising from 30% to 36% rises by 6 percentage points or 20% relative to the original rate.

Comparing Two Percentage Values

For p% and q%, p is greater than q by [(p − q) ÷ q] × 100 when q is the reference percentage.

The percent sign cancels during the calculation, so the same result is obtained by comparing p and q directly. The ratio p:q gives the direct proportional comparison.

Example: 40% is greater than 25% by [(40 − 25) ÷ 25] × 100 = 60%. Their ratio is 40:25 = 8:5.

Reverse Percentage Comparison

If A is x% greater than B, B is not x% less than A; the reverse decrease is calculated using A as the denominator.

If A = B(1 + x/100), then the percentage by which B is less than A is [x ÷ (100 + x)] × 100. Similarly, if A is x% less than B, B is [x ÷ (100 − x)] × 100 greater than A.

Example: If A is 25% greater than B, then B is [25 ÷ 125] × 100 = 20% less than A.

Comparison of Percentages Video Lessons

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Percentage Data Comparison and Reverse Problems

Learn to compare percentage-based data and solve reverse percentage problems by working backward from a given value to determine the original quantity.

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Practice Comparison of Percentages Questions

Practise published questions related to this topic.

1A combo set (mug + coffee beans) is sold at Rs. 600. The mug costs Rs. 250, beans Rs. 280.Find profit or loss %.→ 2A shopkeeper is offering a 15% discount on a shirt whose marked price is ₹1,400. Find the price (in ₹) after the discount.→ 3A trader marked the price of an item 40% above the cost price. He allowed two successive discounts of 20% and 25% to a customer. If he incurred a loss of ₹224, at what price did he sell the item to that customer?→ 4A trader buys an item for ₹500 and gains 20%. What is the selling price?→ 5Two successive discounts of 30 percent and 20 percent are given on an article. If the marked price of the article is Rs. 500, then what is the value of net discount?→ 6Raman purchased a mobile phone marked at Rs. 12000 at successive discounts of 15% and 20% respectively. He spent Rs. 340 on packaging and sold the mobile phone for Rs. 12000. Find his gain percentage (upto two decimals).→ 7Which of the following number is NOT divisible by 4?→ 8The Highest Common Factor of two numbers is 18 and their Least Common Multiple is 540. What is the product of the two numbers?→ 9What is the Least Common Multiple of 4/7, 8/14 and 12/21?→ 10If on a sale, there is 40% discount on the marked price of ₹1,200, but the sale is done at ₹520 only, then how much additional discount did the customer get?→

Comparison of Percentages Quick Quiz

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Quick Revision Notes

Comparison of Percentages: Quick Revision

Use the correct reference value and distinguish percentage points from relative percentage change.

  • Percentage increase from B to A = [(A − B) ÷ B] × 100.
  • Percentage decrease from A to B = [(A − B) ÷ A] × 100.
  • Difference between p% and q% = p − q percentage points.
  • Relative increase of p% over q% = [(p − q) ÷ q] × 100.
  • If A is x% greater than B, B is 100x ÷ (100 + x)% less than A.
  • If A is x% less than B, B is 100x ÷ (100 − x)% greater than A.
  • A percentage comparison changes when the reference denominator changes.

Comparison of Percentages FAQs

What is the formula for comparing two percentages?

If p% is compared with q% using q% as the reference, the relative difference is [(p − q) ÷ q] × 100.

What is the difference between percentage points and percentage change?

Percentage-point difference is direct subtraction: p − q. Relative percentage change is [(p − q) ÷ q] × 100 when q is the original value.

40% is what percent greater than 25%?

The increase is 15 percentage points. Relative to 25%, it is (15 ÷ 25) × 100 = 60% greater.

If one number is 20% greater than another, by what percentage is the smaller number less?

The smaller number is 20 ÷ 120 × 100 = 16⅔% less than the greater number.

If one number is 20% less than another, by what percentage is the greater number more?

The greater number is 20 ÷ 80 × 100 = 25% more than the smaller number.

How do you compare 18% and 24% as a ratio?

Their ratio is 18:24, which simplifies to 3:4. Thus, 18%:24% = 3:4.

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