Introduction:
When two conducting wires of different materials are joined in series across a battery, the drift velocity of electrons in each wire can be different. The drift velocity is the average velocity of electrons in a wire due to the electric field applied by the battery. In this case, we are given that the number density of electrons in wire x is twice that of wire y.

Explanation:
1. Drift velocity: The drift velocity of electrons in a wire can be calculated using the formula:

v = I / (nAe)

where v is the drift velocity, I is the current flowing through the wire, n is the number density of electrons, A is the cross-sectional area of the wire, and e is the charge of an electron.

2. Number density of electrons: The number density of electrons in a wire is the number of electrons per unit volume. In this case, we are given that the number density of electrons in wire x is twice that of wire y.

Therefore, we can write:
n(x) = 2n(y)

3. Diameter and cross-sectional area: The wires x and y have the same diameter. Since the diameter is the same, the cross-sectional area of the wires will also be the same.

4. Current is the same: When two wires are connected in series, the current flowing through each wire is the same. Therefore, we can write:
I(x) = I(y)

Calculating the ratio of drift velocities:
Let's assume the drift velocity in wire x is vx and in wire y is vy.

1. Using the formula for drift velocity, we can write:
vx = I(x) / (n(x)Ae)
vy = I(y) / (n(y)Ae)

2. Since the cross-sectional area of the wires is the same, we can cancel it out from both equations:
vx = I(x) / (n(x)e)
vy = I(y) / (n(y)e)

3. Since the current flowing through each wire is the same, we can equate them:
I(x) = I(y)

4. Substituting the values of I(x) and I(y) in the equations for vx and vy, we get:
vx = I(y) / (n(x)e)
vy = I(y) / (n(y)e)

5. Simplifying the equations, we can write:
vx / vy = (I(y) / (n(x)e)) / (I(y) / (n(y)e))
= (n(y)e) / (n(x)e)
= n(y) / n(x)

6. Substituting the given relation between the number densities of electrons, we get:
vx / vy = n(y) / n(x)
= 1 / 2

Conclusion:
The ratio of the drift velocities of electrons in wires x and y is 1:2. This means that the drift velocity of electrons in wire x is twice that of wire y.