Question

By what number must a given number be multiplied to decrease it by $30\%$?

Answer 1

Hint: We will assume the number as $x$ and then we will find the $30\%$ of the number. Now we will subtract the $30\%$ of the number from number $x$. Then we will assume the number to multiply to decrease the number $x$ to $30\%$ as $y$. From this we will have an equation. By solving the equation, we will get the required value. We know percentage is a number or ratio that can be expressed as a fraction of $100$ which means a part per hundred. The word percent means per $100$. We will calculate the percentage by dividing the value by total value and then multiply it with $100$ to get the percentage. For example we need to calculate the percentage of $2$ in $5$, then $\text{Percentage}=\dfrac{2}{5}\times 100=40\%$, at the same time if you want to calculate the $40\%$ of $5$, then $40\%\text{ of }5=\dfrac{40}{100}\times 5=2$

Complete step-by-step answer:
Let us assume a number as $x$.
$30\%$ of the number is $30\%x=\dfrac{30}{100}x=0.3x$
When we decreased the value of $x$by $30\%$, then the new value is
$\begin{align}
  & x-30\%x=x-0.3x \\
 & =0.7x
\end{align}$
Let the number be multiplied to decrease it by $30\%$ is $y$. i.e. we will get the $30\%$ decreased value of $x$ when $y$ is multiplied to $x$, then
$\begin{align}
  & y\times x=0.7x \\
 & y=0.7
\end{align}$
So, we have to multiply a number with $0.7=\dfrac{7}{10}$ to decrease the number by $30\%$.

Note: We can also find the solution by another method. Let the number is $100\%$ . when it is reduced by $30\%$ the new value is $100\%-30\%=70\%$. i.e. We can find the $70\%$ of the number to get the value when it is reduced by $30\%$ and the number to be multiplied is $70\%=\dfrac{70}{100}=0.7$.
From both methods we get the same result.