If x is 10% less than y, then find the percentage by which y is more than x.


Answer:

 

111
9
 %

Step by Step Explanation:
  1. According to the question, x is 10% less than y.
    This can be written as:
    x = y - (y ×  
    10
    100
     )
  2. From the above equation, we can calculate y in terms of x. In order to do that, we must simplify the equation and rearrange it accordingly.
    Thus,the equation becomes :
    x = y -  
    y
    10
     ,
    which implies, x = y(1 -  
    1
    10
     )
    or, x = y( 
    10 - 1
    10
     )
    or, x =  
    9y
    10
     
    or, y =  
    10x
    9
     
  3. Now, let us try to rewrite the right-hand side of the above equation as a mixed number.
    y = x +  
    x
    9
     
  4. From the above equation, we know that: "y is more than x by a factor of  
    1
    9
     ".
  5. To convert a factor into a percentage, we need to multiply the factor by 100.
    This means that the following two statements mean the same:
    "y is more than x by a factor of  
    1
    9
     ".
    and
    "y is more than x by  
    100
    9
      percent."
  6. On writing the above percentage as a mixed fraction, we get:
    "y is more than x by  
    111
    9
     %
    "

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