Question

How do you calculate the percentage change of $80$ to $24$ ?

Answer 1

Hint: For finding the percentage change of any given number with respect to other number, first of all we need to find the difference between these two numbers and will calculate the difference in number by using subtraction method in which we will subtract smaller number from bigger number. After getting the change or difference in number will convert the obtained difference or change into percentage as (Difference in number/ changed number) \[\times 100\].

Complete step-by-step solution:
Since, we have a pair of numbers that are $80$ and $24$ from the question, where $80$ is the original number and $24$ is the number obtained after change as Original number $=80$ and changed number $=24$
Now, we will calculate the change by using subtraction method in which we will subtract the smaller number from larger number as:
Difference of $80$ and $24$ = larger number (original number) – smaller number (changed number) Difference of $80$ and $24$ $=80-20$
Difference of $80$ and $24$\[=56\]
As we can see that the original number is the larger number and the changed number is the smaller one, the change in these numbers shows that the change is a decrease and it is $56$ in number.
Since, we got the change of the given numbers in number that is a decrease; we will apply the formula of percentage to get this change in percentage as: (Difference in number/ changed number) \[\times 100\]
Now, we will put the respected values in the above formula that we already have as:
\[\Rightarrow \dfrac{56}{80}\times 100\]
Here, we will do the necessary calculation. As we can see that both $56$ and $80$ are the numbers of multiple of $8$ . So, we will eliminate $8$ in these numbers as:
\[\Rightarrow \dfrac{8\times 7}{8\times 10}\times 100\]
\[\Rightarrow \dfrac{7}{10}\times 100\]
Now, we will calculate the product of $7$ and $100$ that is $700$ as:
\[\Rightarrow \dfrac{700}{10}\]
Here, we use division method so that we can get the percentage change in the given numbers as:
\[\Rightarrow 70%\]
Hence, the percentage change of $80$ to $24$ is \[70%\] .

Note: Here, we will try to get the percentage change of the given number by another method as:
Since, we have two numbers that are $80$ and $24$ .
Let assume that the first number is $100%$ in percentage. Now, we will try to get what percentage is $24$ of $80$ as:
$\Rightarrow \dfrac{24}{80}\times 100$
Now, we will do required calculation to get the percentage for $24$ as:
$\Rightarrow \dfrac{8\times 3}{8\times 10}\times 100$
$\Rightarrow \dfrac{3}{10}\times 100$
$\Rightarrow \dfrac{300}{10}$
$\Rightarrow 30%$
Now, we get that $24$ is $30%$ of $80$ .
Since, we have both the values in percentage. So, the change in percentage is difference of those percentages as:
$=100%-30%$
$=70%$
Thus, we got the same result as we got from the solution. Hence, the solution is correct.