If the median of the following distribution is 32•5, then find the values of x and y.

Class & f & cf $\displaystyle 0$-$\displaystyle 10$ & x & x $\displaystyle 10$-$\displaystyle 20$ & $\displaystyle 5$ & \(\displaystyle 5+\mathrm{x}\) $\displaystyle 20$-$\displaystyle 30$ & $\displaystyle 9$ & \(\displaystyle 14+\mathrm{x}\) $\displaystyle 30$-$\displaystyle 40$ & $\displaystyle 12$ & \(\displaystyle 26+\mathrm{x}\) $\displaystyle 40$-$\displaystyle 50$ & y & \(\displaystyle 26+\mathrm{x}+\mathrm{y}\) $\displaystyle 50$-$\displaystyle 60$ & $\displaystyle 3$ & \(\displaystyle 29+\mathrm{x}+\mathrm{y}\) $\displaystyle 60$-$\displaystyle 70$ & $\displaystyle 2$ & \(\displaystyle 31+\mathrm{x}+\mathrm{y}\) Total & $\displaystyle 40$ &\(\displaystyle 31+x+y=40\) \(\displaystyle \Rightarrow \quad \mathrm{x}+\mathrm{y}=9-------(\mathrm{i})\) Median class \(\displaystyle =30-40\) Median \(\displaystyle =32.5=30+\frac{20-(14+\mathrm{x})}{12} \times 10\) \(\displaystyle \Rightarrow \quad \mathrm{x}=3\) \(\displaystyle \Rightarrow \quad \mathrm{y}=6\)