Percentage vs Percentage Points: Difference with Solved Examples

A percentage-point change is the new percentage minus the old percentage. A percentage change divides that difference by the old percentage and multiplies by 100. For example, a score rising from 40% to 50% increases by 10 percentage points, but by 25% relative to the original score.

The two answers describe different comparisons. Use percentage points to compare two rates directly; use percentage change when the question asks how large the change is compared with the starting value.

Percentage and percentage points: the formulas

• Percentage-point change = new rate − old rate.
• Percentage change = (new rate − old rate) ÷ old rate × 100%.

Enter both rates in the same form. For 40% and 50%, use 40 and 50 in the second formula, or use 0.40 and 0.50 consistently. Do not mix 40 with 0.50. A positive result means an increase; a negative result means a decrease.

Example 1: marks improve from 40% to 50%

Suppose a student scores 40 marks out of 100 in one test and 50 out of 100 in another.

1. Find the difference: 50 − 40 = 10.
2. The percentage score increases by 10 percentage points.
3. Compare the difference with the starting score: 10 ÷ 40 × 100 = 25%.

Check: 25% of 40 is 10, and 40 + 10 = 50. Calling this a “10% improvement” would mean an increase of only 4 marks, giving 44 out of 100 instead.

If the tests have different maximum marks, first convert each score into a percentage. For example, 30 out of 50 is 60%, while 70 out of 100 is 70%. The percentage score rises by 10 percentage points, or approximately 16.67% relative to 60%. This compares scores, not necessarily the difficulty of the tests or the student’s learning.

Example 2: a rate falls from 12% to 9%

The direct difference is 9 − 12 = −3 percentage points. The relative change is −3 ÷ 12 × 100 = −25%. Therefore, the rate falls by 3 percentage points, which is a 25% decrease.

Check: one quarter of 12 is 3, so reducing 12 by 25% gives 9. Notice that returning from 9% to 12% requires a 33⅓% increase, not 25%, because the starting value is now 9.

Example 3: a discount changes from 20% to 30%

For a marked price of ₹1,000, a 20% discount saves ₹200 and leaves a selling price of ₹800. A 30% discount saves ₹300 and leaves a selling price of ₹700.

• The discount rate increases by 10 percentage points.
• The discount amount increases by ₹100, which is 50% of ₹200.
• The selling price falls by ₹100, which is 12.5% of ₹800.

All three statements are correct. Each uses a different quantity or starting value. Write down what is changing before choosing the denominator.

What if the starting percentage is zero?

A rise from 0% to 5% is an increase of 5 percentage points. The usual relative percentage-change formula is undefined because it would divide by zero. Do not describe it as a 5% relative increase or invent a finite percentage-change result.

Practice questions with answers

1. Attendance rises from 75% to 90%. Difference: 15 percentage points. Relative increase: 15 ÷ 75 × 100 = 20%. Check: 75 × 1.20 = 90.
2. A rate falls from 8% to 6%. Difference: −2 percentage points. Relative decrease: 2 ÷ 8 × 100 = 25%. Check: 8 × 0.75 = 6.
3. A score rises from 60% to 66%. Difference: 6 percentage points. Relative increase: 6 ÷ 60 × 100 = 10%.
4. A rate of 20% increases by 5% relative to itself. Increase: 20 × 0.05 = 1 percentage point. New rate: 21%. A rise of 5 percentage points would instead give 25%.

How do I choose the right answer in an exam?

Underline the starting value and the wording. If asked for the difference between two percentages, state the percentage-point difference. If asked for percentage increase or decrease, divide the change by the original value. When wording is ambiguous, show both results and label them clearly.

Yaad rakho: percentage points mein seedha difference; percentage change mein starting value se compare karo.

For more worked problems, explore the study blog. If you use DoubtPay to ask a maths question, include your starting value and your attempted calculation so the explanation can address the exact confusing step. AI can make mistakes; check the calculation against your textbook.