Sophia launched her startup 9 years ago. Her present age is $\frac{4}{3}$ times her age when she launched her startup. Sophia’s brother was 12 years younger than her at the time she launched her startup. What is the ratio of Sophia's present age to her brother’s age at the time she launched her startup?

The correct answer is 12:5.

Let Sophia's age at the time she launched her startup be $x$ years.

Since she launched her startup 9 years ago, her present age can be expressed as:

$\text{Present age}=x+9$

According to the question, her present age is $\frac{4}{3}$ times her age when she launched her startup:

$x+9=\frac{4}{3}x$

Subtracting $x$ from both sides to solve for $x$:

$9=\frac{4}{3}x-x$

$9=\frac{1}{3}x$

$x=27$

Thus, Sophia was 27 years old when she launched her startup.

Now, we calculate Sophia's present age:

$\text{Sophia's present age}=27+9=36\text{years}$

We are also given that Sophia's brother was 12 years younger than her at the time she launched her startup:

$\text{Brother's age at startup launch}=27-12=15\text{years}$

Finally, we find the ratio of Sophia's present age to her brother's age at the time she launched her startup:

$\text{Ratio}=\frac{36}{15}$

Dividing both the numerator and denominator by 3 to simplify:

$\text{Ratio}=\frac{12}{5}$

Therefore, the required ratio is 12:5.