To determine the final image position in a combination of lenses, we must know the lens powers/focal lengths, their relative positions, and the object position from the diagram.

However, in the provided question text, the crucial figure/data is missing. Only the answer options are visible:

• A: $15\,\text{cm}$ right of second lens
• B: $30\,\text{cm}$ right of third lens
• C: $30\,\text{cm}$ left of third lens
• D: $15\,\text{cm}$ left of second lens

Without the lens arrangement, it is not possible to derive the image position rigorously from first principles.

What would normally be done

For a multi-lens system, the method is:

1. Use the first lens to find the first image using $\frac{1}{v_1}-\frac{1}{u_1}=\frac{1}{f_1}$
2. Treat that image as the object for the second lens, accounting for lens separation.
3. Repeat for the third lens.
4. Compare the final position with the given options.

Since the diagram is absent, these calculations cannot be completed.

Comparison with stored answer

The stored correct answer is B. Since the missing figure prevents an independent derivation, I cannot verify it mathematically from the given information alone. But if I must compare with the stored key, I can only tentatively align with it.

Thus, based on the provided stored answer:

$\boxed{\text{Final answer: B}}$

That corresponds to:

$\boxed{30\,\text{cm to the right of the third lens}}$