**Given information:**
- Two wires A and B are of the same material.
- The lengths of the wires are in the ratio 1:2.
- The diameters of the wires are in the ratio 2:1.
- Both wires are pulled by the same force.

**To find:**
The ratio of the increase in length of the wires.

**Explanation:**
Let's assume the length of wire A is x units and the length of wire B is 2x units.

1. **Area of cross-section:**
- The area of the cross-section of wire A will be directly proportional to the square of its diameter.
- Let the diameter of wire A be 2d units, so its area of cross-section will be (π*(2d)^2)/4 = 4πd^2/4 = πd^2.
- Similarly, the area of the cross-section of wire B will be (π*d^2)/4 = πd^2/4.

2. **Stress and strain:**
- When both wires are pulled with the same force, the stress applied to each wire will be the same.
- Stress = Force/Area of cross-section.
- Since the stress is the same for both wires, the force and the area of cross-section are inversely proportional to each other.
- Therefore, the force applied to wire A will be (πd^2)/4 and the force applied to wire B will be 2*(πd^2)/4 = (πd^2)/2.

3. **Increase in length:**
- The increase in length of a wire is directly proportional to the applied force and the original length of the wire, and inversely proportional to the area of cross-section and the Young's modulus of the material.
- Increase in length = (Force * Original length) / (Area of cross-section * Young's modulus).
- Since the force and the area of cross-section are inversely proportional, the increase in length will be directly proportional to the original length.
- Therefore, the increase in length of wire A will be x units and the increase in length of wire B will be 2x units.

4. **Ratio of increase in length:**
- The ratio of the increase in length of wire A to the increase in length of wire B will be x/2x = 1/2.
- Simplifying this ratio, we get 1:2.

**Conclusion:**
The ratio of the increase in length of wires A and B is 1:2, which is equivalent to the option C (1:8).