Let the number be $x$.

According to the problem, the number $x$ is greater than its $\frac{2}{5}$th by 24. This can be written as:

$x = \frac{2}{5}x + 24$

To solve for $x$, subtract $\frac{2}{5}x$ from both sides:

$x - \frac{2}{5}x = 24$

Factor out $x$ on the left side:

$\left(1 - \frac{2}{5}\right)x = 24$

Simplify the expression in the parentheses:

$\frac{3}{5}x = 24$

Now, solve for $x$ by multiplying both sides by $\frac{5}{3}$:

$x = 24 \times \frac{5}{3}$

$x = 40$

So, the number is $40$.

Would you like more details, or do you have any questions about this solution?

Here are 5 related questions you might find interesting:

1. What would the equation look like if the number was greater than its $\frac{3}{4}$th by 30?
2. If a number is greater than its $\frac{3}{5}$th by 36, what is the number?
3. How can you check if the solution to the problem is correct?
4. What happens to the equation if the number was less than its $\frac{2}{5}$th by 24?
5. Can you generalize this method to find a number that is greater than its $\frac{m}{n}$th by any given value?

Tip: When solving problems involving fractions, it's often helpful to first isolate the term involving the fraction before solving for the variable.