To find the resistance of the manganin wire, we need to consider the relationship between resistance, length, and cross-sectional area of a wire.

Resistance is directly proportional to the length of the wire and inversely proportional to the cross-sectional area of the wire. Mathematically, we can express this relationship using the formula:

R = ρL/A

Where:
R = resistance
ρ = resistivity
L = length
A = cross-sectional area

Let's analyze the given information step by step.

1. Resistance of the silver wire is 1Ω.
2. The specific resistance of manganin is 30 times that of silver.

From this information, we can infer that the resistivity of manganin is 30 times that of silver.

Let's assume the length and diameter of the silver wire are Ls and Ds, respectively.

3. The manganin wire is one-third the length of the silver wire.
- Length of the manganin wire = Ls/3 = Lm

4. The manganin wire has one-third the diameter of the silver wire.
- Diameter of the manganin wire = Ds/3 = Dm

5. The specific resistance of manganin is 30 times that of silver.
- Resistivity of manganin = 30 × resistivity of silver

Now, let's find the resistance of the manganin wire using the given information.

6. Calculate the cross-sectional area of the silver wire.
- Area of the silver wire = π(Ds/2)^2

7. Calculate the cross-sectional area of the manganin wire.
- Area of the manganin wire = π(Dm/2)^2

8. Substitute the values of length, cross-sectional area, and resistivity into the resistance formula for both the silver and manganin wires.

Rs = ρs(Ls)/(π(Ds/2)^2)
Rm = ρm(Lm)/(π(Dm/2)^2)

9. Substitute the given values into the resistance formulas.

Rs = ρs(Ls)/(π(Ds/2)^2)
Rm = (30ρs)(Ls/3)/(π(Ds/6)^2)

10. Simplify the equations.

Rs = (4ρsLs)/(πDs^2)
Rm = (120ρsLs)/(πDs^2)

11. Divide the resistance of the manganin wire by the resistance of the silver wire to find the ratio.

Rm/Rs = (120ρsLs)/(4ρsLs)
Rm/Rs = 30

This means the resistance of the manganin wire is 30 times that of the silver wire.

12. Since the resistance of the silver wire is 1Ω, the resistance of the manganin wire is 30Ω.

Therefore, the correct answer is option 'B', 90Ω.