Question

How do you find the percentage change from 50 to 82. Indicate whether it is an increase or a decrease. If necessary, round your answer to the nearest percent?

Answer 1

Hint: Here in this question, we have to find the percent of change, to solve this first we have to find the difference between the two numbers and next divide the difference in the original number and multiply the result by 100 to get change in percentage. On simplification we get the required solution.

Complete step by step solution:
In the given question we have to find the percentage change from 50 to 82. And check whether it's an increase or a decrease.
To find the percent of change between two numbers. The first is to find the ratio of the amount of change to the original amount. If the new number is greater than the old number, then that ratio is the percent of increase, which will be a positive. If the new number is less than the old number, then that ratio is the percent of decrease, which will be a negative. So, the first thing to determine when finding the percent of change is whether we are looking at an increase or a decrease.
i.e., \[\% \,change = \dfrac{{change}}{{original}} \times 100\% \]--------(1)
now, find the change or difference between the two numbers
\[ \Rightarrow \,change = 82 - 50\]
\[ \Rightarrow \,change = 32\]
Original value is 50, then by equation (1), we have
\[ \Rightarrow \% \,change = \dfrac{{32}}{{50}} \times 100\% \]
\[ \Rightarrow \% \,change = \dfrac{{32}}{{50}} \times 100\% \]
On simplification, we get
\[ \Rightarrow \% \,change = 0.64 \times 100\% \]
\[ \Rightarrow \% \,change = 64\% \]
Hence, Percentage of change was 64%.
So, the correct answer is “64%”.

Note: The one more method except the above to find the percent of change between two numbers involves finding the ratio between the new number and the original number and multiply the result by 100 and subtract 100 percent from the result. We can also get the same solution. i.e.,
\[ \Rightarrow \% \,change = \dfrac{{new\,value}}{{orginal\,value}} \times 100\% \]
\[ \Rightarrow \% \,change = \dfrac{{82}}{{50}} \times 100\% \]
\[ \Rightarrow 1.64 \times 100\% \]
\[ \Rightarrow 164\% \]
Subtract \[100\% \]
\[ \Rightarrow 164\% - 100\% \]
\[ \Rightarrow 64\% \]
That's the same result as in Method 1: an increase of 64%