Question

What percent of 90 is 15?

Answer 1

Hint: For finding that what percent of 90 is 15 we will use percentage definition. Firstly as we have to what percent of 90 is 15 we will divide 15 by 90 and write them in fraction form. Then we will simplify the numerator and denominator by dividing them with the same number till we get a pair of co-prime numbers. Finally we will multiply the obtained simplified fraction by 100 and get our desired answer.

Complete step by step solution:
To obtain what percent of 90 is 15 we will divide 15 by 90 as follows:
${\displaystyle \frac{15}{90}}$
Now, as we can see that both numerator and denominator have two common factors i.e. 3 and 5
So, we will simplify the above value by dividing the numerator and denominator by 3 and get,
$\begin{array}{rl}& ={\displaystyle \frac{{\displaystyle \frac{15}{3}}}{{\displaystyle \frac{90}{3}}}}\\ & ={\displaystyle \frac{5}{30}}\end{array}$
Again on dividing numerator and denominator by 5 we get,
$\begin{array}{rl}& ={\displaystyle \frac{{\displaystyle \frac{15}{5}}}{{\displaystyle \frac{30}{5}}}}\\ & ={\displaystyle \frac{1}{6}}\end{array}$
$\therefore {\displaystyle \frac{15}{90}}={\displaystyle \frac{1}{6}}$…….$\left(1\right)$
Now, we will multiply right side of the equation (1) by 100 and get,
$\begin{array}{rl}& ={\displaystyle \frac{1}{6}}\times 100\\ & =16.67\mathrm{\%}\end{array}$

Hence 15 is $16.67\mathrm{\%}$ of 90

Note:
Percentage is a term that is widely used in mathematics; it represents a number or a ratio which can be expressed in a fraction of 100. The symbol used to denote is $\mathrm{\%}$. It doesn’t have any dimension therefore it is known as a dimensionless number. It can be represented in both fraction as well as decimal form. We can also use a direct method to find the solution. The formula is:
$P\mathrm{\%}$ of Number $=X$…..$\left(2\right)$
The Number $=90$
$X=15$
Substituting above value in equation (2) we get,
$\begin{array}{rl}& P\mathrm{\%}\times 90=15\\ & {\displaystyle \frac{P}{100}}={\displaystyle \frac{15}{90}}\\ & P={\displaystyle \frac{15}{90}}\times 100\\ & P=16.67\mathrm{\%}\end{array}$