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

 11 1 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
 11 1 9
%
" 