Let's denote John's current age as $3x$ and David's current age as $4x$, based on the given ratio of 3:4.

Four years ago, John's age would have been $3x - 4$ and David's age would have been $4x - 4$.

According to the problem, the ratio of their ages four years ago was 2:3. Therefore, we can set up the following equation:

$$
\frac{3x - 4}{4x - 4} = \frac{2}{3}
$$

Cross-multiplying to solve for $x$:

$$
3(3x - 4) = 2(4x - 4)
$$

Expanding both sides:

$$
9x - 12 = 8x - 8
$$

Subtracting $8x$ from both sides:

$$
x - 12 = -8
$$

Adding 12 to both sides:

$$
x = 4
$$

Now, we can find David's current age by substituting $x$ back into $4x$:

$$
4x = 4 \times 4 = 16
$$

So, David is currently 16 years old.

The correct option is:

16 years

Question

Let's denote John's current age as $3x$ and David's current age as $4x$, based on the given ratio of 3:4.

Four years ago, John's age would have been $3x - 4$ and David's age would have been $4x - 4$.

According to the problem, the ratio of their ages four years ago was 2:3. Therefore, we can set up the following equation:

$$
\frac{3x - 4}{4x - 4} = \frac{2}{3}
$$

Cross-multiplying to solve for $x$:

$$
3(3x - 4) = 2(4x - 4)
$$

Expanding both sides:

$$
9x - 12 = 8x - 8
$$

Subtracting $8x$ from both sides:

$$
x - 12 = -8
$$

Adding 12 to both sides:

$$
x = 4
$$

Now, we can find David's current age by substituting $x$ back into $4x$:

$$
4x = 4 \times 4 = 16
$$

So, David is currently 16 years old.

The correct option is:

16 years

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