# 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.

Therefore,

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

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/

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

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 $b\%$

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