The word 'percentage' is used regularly in the media to describe changes in the interest rate, income tax, VAT, exam results, success rate etc. They are very much part of our lives. |

Mathematically, percentage increase is expressed as

Percentage Increase = $\frac{\text{Increase}}{\text{Original price}}$ * 100%

A change of x percent in a quantity results in a final amount that is 100 + x percent of the original amount. It is the increase as a percentage of the starting value.

### Solved Example

**Question:**Price of a pen increases from $\$$20 to $\$$30. Express this increase as a percentage of the original price.

**Solution:**

New price of pen = $\$$30

Increase = New price of pen - Original price of pen

= $\$$30 - $\$$20

= $\$$10

Formula to find the percentage increase is given as

Percentage Increase = $\frac{\text{Increase}}{\text{Original price}}$ $\times$ 100%

= $\frac{10}{20}$ $\times$ 100%

= 50%

Therefore, there is 50% increase in the original price.

Percentage decrease = $\frac{\text{Decrease}}{\text{Original Number}}$ * 100%

### Solved Example

**Question:**Price of a calculator decreases from $\$$35 to $\$$30. Express the decrease as a percentage of the original number.

**Solution:**

Decrease = Old price - New price

= $\$$35 - $\$$30

= 5

The formula to find the percentage decrease is given as

Percentage decrease = $\frac{\text{Decrease}}{\text{Original Number}}$ * 100%

= $\frac{5}{35}$ * 100%

= 14.28%

**Percentage Increase**

Percentage Increase = $\frac{\text{Increase}}{\text{Original Price}}$ * 100%

**Percentage Decrease**

Percentage decrease = $\frac{\text{Decrease}}{\text{Original Number}}$ * 100%

→ Read More Steps for calculating percentage change is given below:

- Subtract the new given value from the original value.
- Divide the result from the original value.
- Multiply the obtained result by 100% to find the percentage change (Increase/Decrease).

### Solved Examples

**Question 1:**In April, Mark worked a total of 52 hours for 6 days. In May, he worked for 60 hours. By what percentage did Mark's working hours increase in May?

**Solution:**

**Given:**In April, Mark worked for 52 hours.

In May, Mark worked for 60 hours.

Increase = Mark's work hour in May - Mark's work hour in April

= 60 - 52

= 8

The formula to find the percentage increase is

Percentage Increase = $\frac{\text{Increase}}{\text{Original Price}}$ $\times$ 100%

= $\frac{8}{52}$ $\times$ 100%

= 15.38%

Therefore, there is 15.38% increase in the Mark's working hours in May.

**Question 2:**Price of a whole sale fruits decreases from $\$$105 to $\$$80. Express the decrease as a percentage of the original number.

**Solution:**

Decrease = Old price - New price

= $\$$105 - $\$$80

= 25

The formula to find the percentage decrease is given as

Percentage decrease = $\frac{\text{Decrease}}{\text{Original Number}}$ $\times$ 100%

= $\frac{25}{105}$ $\times$ 100%

= 23.81%