Percentage Change Formula: Examples, MCQs and FAQs

Percentage change tells you how much something increased or decreased compared to its original value. It is used in marks, prices, salary hikes, profit-loss, population, and basically everywhere numbers like to show off.

Percentage Change Formula (Simplest Explanation)

Percentage Change Formula

Percentage Change (%) = [(New Value − Old Value) ÷ Old Value] × 100

How to Use the Formula (Step-by-Step)

• Step 1: Find the difference = New Value − Old Value
• Step 2: Divide the difference by the old value
• Step 3: Multiply the result by 100

How to Know if it is an Increase or a Decrease

• If New Value > Old Value, the answer is a percentage increase.
• If New Value < Old Value, the answer is a percentage decrease.
• If New Value = Old Value, the percentage change is 0%.

Shortcut Version (Same Meaning)

• Percentage Increase (%) = [(Increase) ÷ (Original)] × 100
• Percentage Decrease (%) = [(Decrease) ÷ (Original)] × 100

Important Notes (Small but Powerful)

• Old Value is the base. Always divide by the old value, not the new value.
• If Old Value = 0, percentage change cannot be calculated (division by zero).
• A 20% increase and then a 20% decrease does not bring you back to the same value.

3 Sample Questions on Percentage Change (With Solutions)

Question 1: The price of a book increases from 250 to 300. Find the percentage change.

Step 1: Difference = 300 − 250 = 50
Step 2: Divide by old value = 50 ÷ 250 = 0.2
Step 3: Multiply by 100 = 0.2 × 100 = 20%
Answer: 20% increase

Question 2: A student’s marks drop from 80 to 68. Find the percentage change.

Step 1: Difference = 68 − 80 = −12
Step 2: Divide by old value = −12 ÷ 80 = −0.15
Step 3: Multiply by 100 = −0.15 × 100 = −15%
Answer: 15% decrease

Question 3: The population of a town grows from 1,20,000 to 1,50,000. Find the percentage change.

Step 1: Difference = 1,50,000 − 1,20,000 = 30,000
Step 2: Divide by old value = 30,000 ÷ 1,20,000 = 0.25
Step 3: Multiply by 100 = 0.25 × 100 = 25%
Answer: 25% increase

5 MCQs on Percentage Change (With Answers)

Question 1: The percentage change formula is:

a) [(Old − New) ÷ New] × 100
b) [(New − Old) ÷ Old] × 100
c) [(New + Old) ÷ Old] × 100
d) [(New − Old) ÷ New] × 100

Answer:

b) [(New − Old) ÷ Old] × 100

Question 2: A value changes from 40 to 50. The percentage change is:

a) 20% increase
b) 25% increase
c) 20% decrease
d) 25% decrease

Answer:

b) 25% increase

Question 3: A value changes from 90 to 72. The percentage change is:

a) 18% increase
b) 20% increase
c) 18% decrease
d) 20% decrease

Answer:

d) 20% decrease

Question 4: In percentage change, the base value is always:

a) New value
b) Old value
c) Average of old and new
d) The bigger value

Answer:

b) Old value

Question 5: If the old value is 0, the percentage change is:

a) 0%
b) 100%
c) Not defined
d) Always an increase

Answer:

c) Not defined

FAQs on Percentage Change Formula

FAQ 1: What is a percentage change in simple words?

Percentage change shows how much a value increases or decreases relative to its original value, expressed as a percentage.

FAQ 2: Why do we divide by the old value?

Because percentage change is always measured with respect to the original (starting) value. That is the base.

FAQ 3: How do I know if it is an increase or a decrease?

If the new value is greater than the old value, it is an increase. If the new value is smaller, it is a decrease.

FAQ 4: Can percentage change be negative?

Yes. A negative result means the value decreased.

FAQ 5: What if the old value is 0?

The percentage change cannot be calculated because division by zero is not possible.