The equivalent resistance between the points X and Y of the following fig is 

The equivalent circuit is shown in fig. Since the

bridge is balanced, hence the resistance between B and D is in effective.
Resistance of part ABC = 10 + 10 = 20 $\mathrm{\Omega }$
Resistance of pad ADC = 10 + 10 = 20 $\mathrm{\Omega }$
Equivalent resistance E is given by
$\begin{array}{r}\frac{1}{\mathrm{R}}=\frac{1}{20}+\frac{1}{20}=\frac{2}{20}=\frac{1}{10}\\ \mathrm{R}=10\mathrm{\Omega }\end{array}$