In the metre bridge experimental set up, shown in Fig, the null point '$D$' is obtained at a distance of $40 \mathrm{cm}$ from end $A$ of the metre bridge wire. If a resistance of $10 \mathrm{\Omega }$ is connected in series with $X$, null point is obtained at $AD=60 \mathrm{cm}$. Calculate the values of $X$ and $Y$.

Fig. shows experimental setup of a metre bridge. When the two unknown resistances $X$ and $Y$ are inserted, the null point $D$ is obtained $40 \mathrm{cm}$ from the end $A$. When a resistance of $10 \mathrm{\Omega }$ is connected in series with $X$, the null point shifts by $10 \mathrm{cm}$. Find the position of the null point when the $10 \mathrm{\Omega }$ resistance is instead connected in series with resistance '$Y$'. Determine the values of the resistances $X$ and $Y$.