Question

If \[x\] is \[90\% \] of \[y\], then \[y\] is what percent of \[x\]?
A. \[101\% \]
B. \[190\% \]
C. \[90\% \]
D. \[111.11\% \]

Answer 1

Hint:
Here we will firstly write the value of the \[x\] in terms of the \[y\] in the equation form. Then we will solve it to get the value of \[y\] in terms of \[x\]. Then we will multiply it with 100 to get \[y\] in terms of the percentage of \[x\].

Complete Step by step Solution:
It is given that \[x\] is 90% of \[y\].
Now we will write it in the form of the equation. Therefore, we get
\[x = 90\% \times y\]
Now we will expand the percentage and solve it to get it in the lowest form. Therefore, we get
\[ \Rightarrow x = \dfrac{{90}}{{100}} \times y\]
Dividing the terms, we get
\[ \Rightarrow x = \dfrac{{9y}}{{10}}\]
Now we will use the above equation to get the value of \[y\] in terms of \[x\].
On cross multiplication, we get
\[ \Rightarrow y = \dfrac{{10x}}{9}\]
Now we will multiply the above equation by 100 to get it in terms of the percentage. Therefore, we get
\[ \Rightarrow y = \dfrac{{10x}}{9} \times 100 = \dfrac{{1000x}}{9}\]
Dividing 1000 by 9, we get
\[ \Rightarrow y = 111.11\% \times x\]
Hence the value of y is \[111.11\% \] percent of \[x\].

So, option D is the correct option.

Note:
While calculating the percentage of something we have to multiply the ratio with 100 to get it in terms of percentage. Percentage of a variable is equal to the ratio of the value of the variable to the total value of the variable and multiplies it with 100 to get the required percentage of the variable. Percentage can be represented in both decimal and fraction form. In real life, we use percentages to show the marks obtained by students, depicting humidity etc.