When a number is increased by 24, it becomes $110\%$ of itself. What is the number?

Let the number be $x$.According to the question, when the number is increased by 24, it becomes $110\%$ of itself:
$$x+24=\frac{110}{100}\cdot x$$
Simplify the equation:
$$x+24=1.1x$$
$$24=1.1x-x$$
$$24=0.1x$$
$$x=\frac{24}{0.1}=240$$
Thus, the number is 240.