Percentage Changing

The change in the value of an item can be expressed as a percentage increase or decrease of the original value.
An increase of 5% in the salary of a ma n who earns Rs.500 per month means there is an increase of Rs.5 for every hundred (100); i.e. after the increase, Rs.100 becomes 105.


\[\underline {\begin{array}{*{20}{c}} {100}&{}&{{\text{becomes}}}&{}&{{\text{105}}} \\ {{\text{100}}}&{}&{{\text{becomes}}}&{}&{{\text{105}}} \\ {{\text{100}}}&{}&{{\text{becomes}}}&{}&{{\text{105}}} \\ {{\text{100}}}&{}&{{\text{becomes}}}&{}&{{\text{105}}} \\ {{\text{100}}}&{}&{{\text{becomes}}}&{}&{{\text{105}}} \end{array}} \]
\[\begin{array}{*{20}{c}} {500}&{}&{{\text{becomes}}}&{}&{{\text{525}}} \end{array}\]
\[\begin{array}{*{20}{c}} {{\text{New Salary}}}&{}&{\text{:}}&{}&{{\text{Original Salary}}} \\ {{\text{105}}}&{}&{\text{:}}&{}&{{\text{100}}} \\ {\frac{{{\text{New Salary}}}}{{{\text{Original Salary}}}}}&{}& = &{}&{\frac{{105}}{{100}}} \end{array}\]

New Salary = $$\frac{{105}}{{100}}$$ x Original Salary = $$\frac{{105}}{{100}}$$ x 500 = 525

On the other hand, a decrease of 5% in his salary means that for every Rs.100 in the original salary, there is a decrease of Rs.5; i.e. each Rs.100 becomes Rs.95/

                        \[\underline {\begin{array}{*{20}{c}} {100}&{}&{{\text{becomes}}}&{}&{{\text{95}}} \\ {{\text{100}}}&{}&{{\text{becomes}}}&{}&{{\text{95}}} \\ {{\text{100}}}&{}&{{\text{becomes}}}&{}&{{\text{95}}} \\ {{\text{100}}}&{}&{{\text{becomes}}}&{}&{{\text{95}}} \\ {{\text{100}}}&{}&{{\text{becomes}}}&{}&{{\text{95}}} \end{array}} \]
\[\begin{array}{*{20}{c}} {500}&{}&{{\text{becomes}}}&{}&{{\text{475}}} \end{array}\]
$$\therefore \frac{{{\text{New Salary}}}}{{{\text{Original Salary}}}} = \frac{{95}}{{100}}$$

New Salary = $$\frac{{95}}{{100}}$$ x Original Salary = $$\frac{{95}}{{100}}$$ x 500 = 475

In general,

If an amount “$$a$$” is increased by $$b\% $$
$$\therefore \boxed{{\text{New Amount = }}\frac{{{\text{(a + 100)}}}}{{{\text{100}}}}{\text{ x (}}a{\text{)}}}$$

If an amount “$$a$$” is decreased by $$b\% $$

$$\therefore \boxed{{\text{New Amount = }}\frac{{{\text{(a – 100)}}}}{{{\text{100}}}}{\text{ x (}}a{\text{)}}}$$