Answer
Verified
376.2k+ views
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,
$\Rightarrow x$ % = $\dfrac{x}{100}$
Now, the term ‘of’ means multiplication in mathematics, so according to the question we must have,
$\Rightarrow \dfrac{x}{100}\times 85=17$
Solving the above equation for the value of x we get,
\[\Rightarrow x=\dfrac{17\times 100}{85}\]
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.
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,
$\Rightarrow x$ % = $\dfrac{x}{100}$
Now, the term ‘of’ means multiplication in mathematics, so according to the question we must have,
$\Rightarrow \dfrac{x}{100}\times 85=17$
Solving the above equation for the value of x we get,
\[\Rightarrow x=\dfrac{17\times 100}{85}\]
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.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Change the following sentences into negative and interrogative class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Application to your principal for the character ce class 8 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE