Question

What number is $15\%$ of $80\;$ ?

Answer 1

Hint: To solve these questions, assume the number as a variable and then form an appropriate equation of the given condition in the question. The percentage can be described as a ratio or a number which is expressed as the fraction of $100\;$

Complete step by step solution:
It is given in the question that,
We have to find the number that will be the same as $15\%$ of $80$ .
Let us assume that number to be $x$. Now, the number $x$ is to $80$ as $15$ is to $100$. We have taken $100$ here, since percentages are calculated over a fraction of $100$.
Therefore, from the above relation, we can get the equation as,
$\dfrac{x}{15}=\dfrac{80}{100}$
Now, let us cross multiply the above fractions to get the equation given below,
$\Rightarrow x\times 100=15\times 80$
Multiply the above terms to simplify the equation, to get,
$\Rightarrow 100x=1200$
Now, we divide both the sides of the equation by $100$, to get,
$\Rightarrow \dfrac{100x}{100}=\dfrac{1200}{100}$
On cancelling the zeroes in both the numerators and denominators of the fractions on both the sides, we get,
$\Rightarrow x=12$
Hence, we get the value of the variable as $12$
Therefore, $15\%$ of $80$ is the number $12$

Note: In the solution that is given above, the word percentage or percent can be described as the ratio of a number to $100\;$. It is represented by the symbol $\%$ . For example, if we take a fractional number $0.02\;$then in percent it can be written as $2\%$ .
We can also check if our answer is correct by substituting the value of the variable back in the equation and checking if both the sides are the same or not.
Therefore, substituting $x=12$ in the equation $100x=1200$ we get,
$\Rightarrow 100\times 12=1200$
$\Rightarrow 1200=1200$
Therefore, we can see that both the sides of the equation are the same and hence we can say that our answer is correct.