Given:
Mass of methane = mass of ethane
Total translational kinetic energy of methane : total translational kinetic energy of ethane = 3 : 1

To find:
Ratio of temperatures of methane and ethane

Solution:
The translational kinetic energy of a gas is given by the equation:

KE = (3/2) * (nRT)

where KE is the kinetic energy, n is the number of moles, R is the ideal gas constant, and T is the temperature.

Step 1:
Since the mass of methane is equal to the mass of ethane, we can assume that the number of moles of methane is equal to the number of moles of ethane.

Step 2:
Let's assume that the mass of methane and ethane is m grams. Therefore, the number of moles of methane and ethane can be calculated as:

Number of moles = mass / molar mass

Since the molar mass of methane is 16 g/mol and the molar mass of ethane is 30 g/mol, the number of moles of methane and ethane is the same.

Step 3:
Let's assume the temperature of methane is T1 and the temperature of ethane is T2.

Therefore, the kinetic energy of methane can be written as:

KE1 = (3/2) * (n * R * T1)

And the kinetic energy of ethane can be written as:

KE2 = (3/2) * (n * R * T2)

Since the total translational kinetic energy of methane is 3 times that of ethane, we can write the equation:

KE1 + KE2 = 3 * KE2

Substituting the values of KE1 and KE2, we get:

(3/2) * (n * R * T1) + (3/2) * (n * R * T2) = 3 * (3/2) * (n * R * T2)

Step 4:
Simplifying the equation, we get:

T1 + T2 = 3 * T2

T1 = 2 * T2

Therefore, the ratio of temperatures of methane and ethane is 2:1, which can be simplified to 8:5.

Answer:
The ratio of temperatures of methane and ethane is 8:5. Therefore, the correct option is (d) 8:5.