In the below diagram, calculate the ratio of the resistances A, B, C and D.

Let resistance of wire D be R.

Resistance of wire A (R_A) = $\dfrac{\text R}{4}$
∵ If the diameter of a wire is doubled, the resistance becomes one-fourth of its initial value.

Resistance of wire B (R_B) = 3R
∵ If the length of a wire becomes three times its original length, the resistance becomes three times the initial resistance.

Resistance of wire C (R_C) = $\dfrac{\text R}{2}$
∵ If both the length and diameter of a wire are doubled, the resistance becomes half of its initial value.

Ratio of resistances = $\text{R}$\text{A} : \text{R}\text{B} : \text{R}\text{C} : \text{R}\text{D} = \dfrac{\text R}{4}:3\text R:\dfrac{\text R}{2}:\text R

Multiplying all the terms with LCM of 4 and 2 (i.e., 4) we get,

$\text{R}$\text{A} : \text{R}\text{B} : \text{R}\text{C} : \text{R}\text{D} = 1 : 12 : 2 : 4

∴ Ratio of the resistances A, B, C and D = 1 : 12 : 2 : 4