Question

What percent of 27.5 is 17.16?

Answer 1

Hint: Assume that x percent of 27.5 is 17.16. Now, convert x percent into fraction by dividing x with 100. Multiply this obtained fraction with 27.5 and equate it with 17.16. Form a linear equation in x and solve it for the value of x to get the answer.

Complete step by step answer:
Here we have been provided with two decimal numbers: 27.5 and 17.16 and we are asked to determine the percentage of 27.5 that will make 17.16. First let us understand the meaning of the term ‘percentage’.
In mathematics, percentage represents a number or ratio as a fraction of 100. For example: if we write 25% then we mean in a total of 100 parts of something we have mentioned 25 parts. To change a percentage into the fraction we divide the given percentage by 100 and remove the percentage sign.
Now let us come to the question. Assuming that $x\%$ of 27.5 is 17.16 we have,
$\Rightarrow x\%=\dfrac{x}{100}$
According to the question we must have,
$\Rightarrow \dfrac{x}{100}\times 27.5=17.16$
Solving the above equation for the value of x we get,
\[\Rightarrow x=\dfrac{17.16\times 100}{27.5}\]
Removing the decimal point and simplifying the expression by cancelling the common factors we get,
\[\begin{align}
  & \Rightarrow x=\dfrac{1716\times 100}{275}\times \dfrac{10}{100} \\
 & \Rightarrow x=\dfrac{17160}{275} \\
 & \therefore x=62.4 \\
\end{align}\]

Hence, 62.4% of 27.5 is 17.16.

Note: You must remember the basic definition of percentage to solve the above question. Note that if we have to convert a decimal or fraction into the percentage then we multiply it with 100 and include a percentage sign. Since percentage is a fraction multiplied with 100, so it is dimensionless in nature. It means percentage has no units and is a pure number.