# The number $ 60 $ is reduced to $ 45 $ . What is the percentage decrease in the number? If a number increases by $ 10\% $ and the resulting number is again increased by $ 10\% $ . What is the percentage increase finally?

Answer

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**Hint**: Percent: Percent or percentage is used in mathematics as the number or ratio which is expressed as a fraction of a hundredth. And this is followed by the sign ‘%’. Percentage has no dimension. Hence it is called dimensionless. Every percentage variable has three possible unknown variables: percentage, part, base.

We go step by step wise as given in question. We should find the percentage of change with respect to the base term.

**Complete step by step solution:**

Given,

First number $ = 60 $

Second number $ = 45 $

$ \Rightarrow Reduction{\text{ }}in{\text{ }}the{\text{ }}number = First\,number - \sec ond\,number $

$ \Rightarrow Reduction{\text{ }}in{\text{ }}the{\text{ }}number = 60 - 45 $

$ \Rightarrow Reduction{\text{ }}in{\text{ }}the{\text{ }}number = 15 $

Percentage decrease in number is given by

$ \Rightarrow Percentage\,Decrease = \dfrac{{\operatorname{Re} duction\,in\,number}}{{First\,number}} \times 100 $

$ \Rightarrow Percentage\,Decrease = \dfrac{{15}}{{60}} \times 100 $

$ \Rightarrow Percentage\,Decrease = \dfrac{1}{4} \times 100 $

$ \Rightarrow Percentage\,Decrease = 25\% $

Hence percentage decrease in number is $ = 25\% $

Now the two successive increase respectively $ a\,and\,b $ in number is given in percentage then,

$ \Rightarrow Total\,increase = a + b + \dfrac{{a \times b\,}}{{100}} $

Here given

$ first\,number,\,a = 10\% $

$ \sec ond\,number,b = 10\% $

Put the value in formula then we get

$ \Rightarrow Total\,increase = 10 + 10 + \dfrac{{10 \times 10\,}}{{100}} $

$ \Rightarrow Total\,increase = 20 + 1 $

$ \Rightarrow Total\,increase = 21% $

**Note**: Percentage is widely used in profit and loss. It is also used to show statistics data to increase or decrease in data by how much percentage. The percentage function takes the form z is equal to the x percent of number y. Taking a percent can be viewed as the same operation as multiplication by a fraction.

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