When 75 is added to the 75% of a number, it gives the same number. Find the number?

Hint: We will first assume the number we want to find. Then try to make an equation using the relations given in the question. We will use general methods to simplify and get the value of the variable. We should also be familiar with methods like substitution, elimination etc. for solving the equations.

Complete step-by-step solution:
We will first assume the number is x.
We can write 75% of a number as
$ = 75\% \times \,x$
$ = \dfrac{{75x}}{{100}}$
When we add 75 to the 75% of the number, we get
$ = \dfrac{{75x}}{{100}} + 75$
Since we have given when 75 is added to 75% of the number, we get the same number.
We can write
$ \Rightarrow \dfrac{{75x}}{{100}} + 75 = x$
We simplify the equation, by dividing $\dfrac{{75x}}{{100}}$ by 25
$ \Rightarrow \dfrac{{3x}}{4} + 75 = x$
We transpose $\dfrac{{3x}}{4}$ to the right side
$ \Rightarrow 75 = x - \dfrac{{3x}}{4}$
$ \Rightarrow 75 = \dfrac{x}{4}$
$ \Rightarrow x = 300$
So, the number when 75 is added to 75% of the number, we get the same number is 300.

Note: We can easily solve the equation, but the most important thing is finding the relation between the variables. Sometimes, it becomes easy to find the relation if we assume two variables. Then using the substitution method, we will substitute another variable in terms of the first variable.