Question

If a number $x$ is 10% less than another number $y$ and $y$ is 10% more than 125, then $x$ is equal to ?

Answer 1

Hint: Form the equation using statement then find out $x$. To find $x$ you have to first find $y$ as the full statement of $y$ is given.

Complete step by step answer :
Let us consider $y$ first, here $y$ is 10 % more than 125 that implies
$y = 125 + 10\% $ of 125 ………………………..(1)
% of 125, here “of” means multiplication that is 10% $ \times $ 125
and now let’s consider the number $x$ , here $x$ is less than another number $y$ which means, $x$ is only 90% of $y$.
$x = y - 10\% $ of $y$ ………………………..(2)
% of $y$, here “of” means multiplication that is 10% $ \times $$y$ , convert the percent by dividing the given percent by 100
Solving the equation of $y$ first,
$ \Rightarrow y = 125 + \dfrac{{10}}{{100}} \times 125$
Multiply and add the above , we get
$
   \Rightarrow y = \dfrac{{1250 + 125}}{{10}} \\
   \Rightarrow y = \dfrac{{1375}}{{10}} \\
   \Rightarrow y = 137.5 \\
 $
Putting the value of $y$ in equation 2 to find the value of $x$
$ \Rightarrow x = 137.5 - 10\% \times 137.5$
Convert the percent by dividing the given percent by 100
$ \Rightarrow x = 137.5 - (\dfrac{{10}}{{100}} \times 137.5)$
Solving the parenthesis first that is solving the bracket part first,
$ \Rightarrow x = 137.5 - (13.75)$
Subtract the above and remove bracket

$ \Rightarrow x = 123.75$

Note:
Percent always has a base value which means we are always expressing a percent of something.
When we write 10% or any percent more than, the base value is the starting, smaller value or smaller number. When we write 10% or any percent less than, the base value is the starting , larger value or larger number.
In this question, $x$ is only 90% of $y$ as $x$ is less than $y$.