Question

State whether the statement is True or False. $12\%$ of $120$ are $100$.
A) True
B) False

Answer 1

Hint: To solve this type of question we need to know the concept of percentage. The question requires conversion of percentage into fraction and vice-versa. We will be multiplying the fraction found with the number given to us which is $120$, and check whether the result comes to $100$ or not.

Complete step by step answer:
The question asks to check whether $12\%$ of $120$ gives $100$ . To check whether the statement is true or false we will find the value of $12\%$ of $120$. If the result comes the same as $100$, then the statement is true else it is false. To solve this the first step will be to change the percentage into fraction the value of $x$. Since $12\%$ is a percentage, so it will be divided by $100$ to change the percentage into fraction, on doing this we get:
$\Rightarrow 12\%=\dfrac{12}{100}$
So on substituting the percentage with the fraction, and writing the equation becomes:
$\Rightarrow \dfrac{12}{100}\times 120$
On multiplying the numerator terms together
$\Rightarrow \dfrac{12\times 120}{100}$
On calculating further the above expression we will get:
$\Rightarrow \dfrac{1440}{100}$
$\Rightarrow \dfrac{144}{10}$
Now, since the above statement has $10$ as the denominator, changing the fraction into decimal becomes easier. So the decimal form of the fraction is:
$\Rightarrow 14.4$
$12\%$ of $120$ is $14.4$ and not $100$.
$\therefore $ The statement $12\%$ of $120$ are $100$ is B) False.

Note: Let us check whether the answer we got is correct or not. For this we would perform the particular task. Let's check what percentage is $14.4$ of $120$. which mathematically could be written as
$\Rightarrow \dfrac{14.4}{120}\times 100$
On multiplying the numerator terms together
$\Rightarrow \dfrac{1440}{120}$
$\Rightarrow 12$
This shows that the percentage for $14.4$ of $120$ is $12\%$.