The circuit is a balanced Wheatstone bridge because the ratio of resistances in both branches is equal: 10Ω/20Ω = 10Ω/20Ω. In a balanced bridge, no current flows through the middle resistor (15Ω), so it can be ignored for calculating equivalent resistance.

The circuit simplifies to two parallel paths between X and Y. Each path has two series resistors: (10Ω + 20Ω) = 30Ω. The equivalent resistance of two 30Ω resistors in parallel is:

$\frac{1}{R_{eq}}=\frac{1}{30}+\frac{1}{30}=\frac{2}{30}=\frac{1}{15}$

Therefore, $R_{eq}=15\mathrm{\Omega }$.

Final Answer: $15\mathrm{\Omega }$