Question

What percent of 85 is 17?

Answer 1

Hint: Assume that x percent of 85 is 17. Now, convert x percent into fraction by dividing x with 100 and removing the percent sign. Multiply this obtained fraction with 85 and equate it with 17. Form a linear equation in x and solve it for the value of x to get the answer.

Complete step by step solution:
Here we have been asked to determine a percentage of 85 that will be equal to 17. But first we need to 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 45% of total students in a class failed in science then it means if there are 100 students in the class then 45 of them failed in science while the other 55 passed. To change a percentage into fraction we divide the given percentage by 100 and remove the percentage sign.
Now let us come to the question. Let us assume $x$ % of 85 is 17. So converting $x$ % into fraction we get,
$\Rightarrow x$ % = ${\displaystyle \frac{x}{100}}$
Now, the term ‘of’ means multiplication in mathematics, so according to the question we must have,
$\Rightarrow {\displaystyle \frac{x}{100}}\times 85=17$
Solving the above equation for the value of x we get,
$$\Rightarrow x={\displaystyle \frac{17\times 100}{85}}$$
Cancelling the common factors and simplifying the relation we get,
$$\therefore x=20$$
Hence, 20% of 85 is 17.

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 that means percentage has no units and is a pure number.