Question

What is $30\mathrm{\%}$ of $80$?

Answer 1

Hint: Now let us say 30% of 80 is x. then we know that the ratio ${\displaystyle \frac{x}{80}}$will be equal to ${\displaystyle \frac{30}{100}}$ . Now we will solve the equation ${\displaystyle \frac{x}{80}}={\displaystyle \frac{30}{100}}$ and find the value of x. Hence we will find the value of $30\mathrm{\%}$ of 80.

Complete step by step solution:
Now let us first understand the concept of percentage.
Percent translates to per 100. Hence percentage is a number which denotes parts per 100.
Percentages are nothing but fractions with denominator 100.
Let us understand this by an example.
Suppose we want to represent 30 out of 100 by a number. Then this can be written as ${\displaystyle \frac{30}{100}}$ or $30\mathrm{\%}$ .
Similarly suppose we have 20 out of 50. Then in fractional form we write it as ${\displaystyle \frac{20}{50}}$ Now multiplying the numerator and denominator of the above fraction by 2 we get ${\displaystyle \frac{40}{100}}$ . Hence we can write it as $40$.
Now let us say 30 percent of 80 is x. Consider the ratio ${\displaystyle \frac{x}{80}}$ which denotes x parts out of 80.
Now we know that percentage is nothing but fraction with denominator 100.
Hence we can say that the ratio ${\displaystyle \frac{x}{80}}$ is equal to ${\displaystyle \frac{30}{100}}$ .
Now consider the equation ${\displaystyle \frac{x}{80}}={\displaystyle \frac{30}{100}}$ .
Cross multiplying the terms in the above equation we get,
$\begin{array}{rl}& \Rightarrow 100x=80\times 30\\ & \Rightarrow 100x=2400\end{array}$
Now dividing the whole equation by 100 we get,
$\Rightarrow x=24$
Hence we get 30 percent of 80 is 24.

Note: Now note that we can write $30\mathrm{\%}$ as ${\displaystyle \frac{30}{100}}$ . Now to find $30\mathrm{\%}$ of 80 we can simply multiply the fraction representing the percentage by 80. Hence we can find the value by solving the expression ${\displaystyle \frac{30}{100}}\times 80$ .