Question

What is the percentage change when $64$ is increased to $144$ ?

Answer 1

Hint: In the given question, we are required to calculate the percentage change in a number when we are given that a certain quantity has been increased to a new number. So, we can find the change in number by subtracting the original number from the new or the increased form of the number. Then, we will have to find the percent of change in the number. The percentage of change in a number can be calculated by the formula: $Change\mathrm{\%}={\displaystyle \frac{Change}{Original}}\times 100\mathrm{\%}$ .

Complete step by step solution:
In this specific question, we are given that the number $64$ is increased to $144$ and we have to calculate the percentage increase in the number.
So, we first find the change in the number by subtracting the original number from the new or thr increased final number.
So, we get the change in number as $144-64=80$ .
Now, we have to find the change percent in the situation.
So, we have to find what percent of the original number $64$ corresponds to the change in the number, that is, $80$ .
So, we can find the change percent in the number using the standard formula
$Change\mathrm{\%}={\displaystyle \frac{Change}{Original}}\times 100\mathrm{\%}$ .
So, we get, $Change\mathrm{\%}={\displaystyle \frac{80}{64}}\times 100\mathrm{\%}$
Cancelling the common factors in numerator and denominator, we get,
 $\Rightarrow Change\mathrm{\%}={\displaystyle \frac{10}{8}}\times 100\mathrm{\%}$
Now, carrying out the multiplication in the numerator of the fraction and simplifying the expression, we get,
 $\Rightarrow Change\mathrm{\%}={\displaystyle \frac{1000}{8}}\mathrm{\%}$
Cancelling the common factors in numerator and denominator, we get,
 $\Rightarrow Change\mathrm{\%}=125\mathrm{\%}$
So, the percentage change when $64$ is increased to $144$ is $125\mathrm{\%}$ .
This is our required final answer for the given problem.
So, the correct answer is “ $125\mathrm{\%}$ ”.

Note: There are various methods to find an answer to the given question, but the method described above is the simplest one. We can also consider solving the problem using the unitary method by taking the original number as $100\mathrm{\%}$ of itself and then computing the change percent in comparison to the original number. Work as many problems as possible to crack these types of problems in a limited time period.