Find the percentage change, when a number is changed from :

(i) 80 to 100

(ii) 100 to 80

(iii) 6.25 to 7.50

(i) 80 to 100

Given:

Initial Number = 80

Final Number = 100

Increase in number = Final number - Initial number

Increase in number = 100 - 80 = 20

Percentage Increase = $\dfrac{\text{Increase in number}}{\text{Initial Number}} \times 100$ %

= $\dfrac{20}{80} \times 100$ %

= $\dfrac{2,000}{80}$ %

= 25%

The percentage increase = 25 %.

(ii) 100 to 80

Given:

Initial Number = 100

Final Number = 80

Decrease in number = Initial number - Final number

Decrease in number = 100 - 80 = 20

Percentage Decrease = $\dfrac{\text{Decrease in number}}{\text{Initial Number}} \times 100$ %

= $\dfrac{20}{100} \times 100$ %

= $\dfrac{2,000}{100}$ %

= 20%

The percentage decrease = 20 %.

(iii) 6.25 to 7.50

Given:

Initial Number = 6.25

Final Number = 7.50

Increase in number = Final number - Initial number

Increase in number = 7.50 - 6.25 = 1.25

Percentage Increase = $\dfrac{\text{Increase in number}}{\text{Initial Number}} \times 100$ %

= $\dfrac{1.25}{6.25} \times 100$ %

= $\dfrac{125}{6.25}$ %

= $\dfrac{12,500}{625}$ %

= 20%

The percentage increase = 20 %.