Question

A number is increased by $10\% $ becomes $62$ . What will it become if it is decreased by $20\% $ .

Answer 1

Hint: Percent: Percent or percentage is used in mathematics as the number or ratio which is expressed as fraction of 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.
To solve this we should take a variable as a number and apply the given condition and get the final answer.

Complete step-by-step answer:
Given,
Number increased by %, a $ = 10\% $
Number get, b $ = 62$
Number decreased by, c $ = 20\% $
Final number=?
According to question
$10\% \,of\,x\,\,is\,62.$
\[ \Rightarrow \dfrac{{10}}{{100}} \times x = 62\]
Simplify
\[ \Rightarrow 10 \times x = 62 \times 100\]
By cross multiplication,
\[ \Rightarrow x = \dfrac{{62 \times 100}}{{10}}\]
\[ \Rightarrow x = 62 \times 10\]
\[ \Rightarrow x = 620\]
Hence the first number is $620$.
When it will decrease by $20\% $
$20\% \,of\,620$
\[ \Rightarrow y = 620 \times \dfrac{{20}}{{100}}\]
Simplify
\[ \Rightarrow y = 124\]
\[ \Rightarrow Final\,number = First\,number - y\]
Put the value
\[ \Rightarrow Final\,number = 620 - 124\]
\[ \Rightarrow Final\,number = 496\]
The final number is $496$
So, the correct answer is “ $496$ ”.

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.