Percentages Formulas

1. Per cent is Per 100. Cent is 100.

The symbol for percent is %.

The fraction 1/100 is written for %

So, 50% is 50 × 1/100 = 50/100 = ½

2. Formulas on Percent Change:

1. Percent Increase is

(amount of increase/initial number) × 100%

2. Percent Decrease is

(amount of decrease/initial number) × 100%

3. Formulas on Percent Comparison:

1. Percent Greater (more) is

(difference of the numbers)/(smaller number) × 100%

2. Percent Smaller (less) is

(difference of the numbers)/(greater number) × 100%

4. Formulas on Percent (total) change during successive percent changes:

Note: In the following, + sign denotes increase, and – sign, decrease.

1. If a number N is increased first by x% and next by y%, then the total percent

change is

(x + y + (x y/100))%

2. If a number N is decreased first by x% and increased next by y%, then the total percent

change is

(- x + y - x y/100)%

3. If a number N is increased first by x% and decreased next by y%, then the total percent

change is

(+x – y –xy/100)%

5. Formulas on Three important concepts on percents:

1. Consider a number N.

It is successively increased twice by x% each time.

Then, the total percent increase is > 2x%

2. Consider a Number N.

It is successively decreased twice by x% each time.

Then, the total percent decrease is < 2x%

3. Consider a Number N.

It is successively increased and decreased by x% each time.

Then, the final value is less than the original value.