To convert the given Delta network to its equivalent Y network, we use the following formulas:

• \(R_1 = \frac{R_{ab} \cdot R_{ac}}{R_{ab} + R_{bc} + R_{ca}}\)
• \(R_2 = \frac{R_{ab} \cdot R_{bc}}{R_{ab} + R_{bc} + R_{ca}}\)
• \(R_3 = \frac{R_{bc} \cdot R_{ca}}{R_{ab} + R_{bc} + R_{ca}}\)

Here, \(R_{ab} = 30 \, \Omega\), \(R_{bc} = 50 \, \Omega\), and \(R_{ca} = 20 \, \Omega\).

Let's calculate each resistance:

Calculate \(R_1\):

\(R_1 = \frac{30 \cdot 20}{30 + 50 + 20} = \frac{600}{100} = 6 \, \Omega\)

Calculate \(R_2\):

\(R_2 = \frac{30 \cdot 50}{30 + 50 + 20} = \frac{1500}{100} = 15 \, \Omega\)

Calculate \(R_3\):

\(R_3 = \frac{50 \cdot 20}{30 + 50 + 20} = \frac{1000}{100} = 10 \, \Omega\)

Therefore, the resistances \(R_1\), \(R_2\), and \(R_3\) are respectively \(6 \, \Omega\), \(15 \, \Omega\), and \(10 \, \Omega\).

Thus, the correct answer is 6 \(\Omega\), 15 \(\Omega\) and 10 \(\Omega\).