Question

What is the percentage of increase of 50 to 90 ?

Answer 1

Hint: The percent of increase of a number can be done by calculating the percentage of “increase” in the number with the number itself. The increase can be calculated by subtracting the initial number by the increased number and its percentage can be calculated by dividing it with the original number and multiplying it by hundred.

Complete step-by-step answer:
Let us first calculate the increase in the initial number. We have been given to us, the initial number as 50 and the increased number as 90. So, on subtracting 50 from 90, we can calculate the increase in the number. Mathematically, this could be done as follows:
$\begin{align}
  & =90-50 \\
 & =40 \\
\end{align}$
Now, let us denote this increase by ‘x’ such that we have:
$\Rightarrow x=40$
Let us name the above equation as (1). So, we have:
$\Rightarrow x=40$ ......... (1)

Then, the increase percentage can be calculated by dividing the increase with the initial number and then multiplying it by hundred. Mathematically, this could be done as follows:
Let the increased percentage be ‘y’. Then, we have:
$\Rightarrow y=\dfrac{x}{50}\times 100$
Using the value of ‘x’ from equation number (1), we get:
$\begin{align}
  & \Rightarrow y=\dfrac{40}{50}\times 100 \\
 & \Rightarrow y=\dfrac{4000}{50} \\
 & \Rightarrow y=80\% \\
\end{align}$

Thus, the final increase in percentage comes out to be 80%.
Hence, the percent of increase of 50 to 90 is 80%.

Note: Whenever, we calculate the percentage of any quantity, that is, of a fraction or a decimal, it is always a non-negative term. Another interesting property of percentage is that the terms in it can be reversed, that is, x% of y is equal to y% of x. For example: 10% of 100 is equal to 10 and 100% of 10 is also equal to 10. It can be used to get a faster solution to our problem.