Following distribution shows the marks of 230 students in a particular subject. If the median marks are 46, then find the values of x and y.

Marks	Number of Students	Cf
$\displaystyle 10$-$\displaystyle 20$	$\displaystyle 12$	$\displaystyle 12$
$\displaystyle 20$-$\displaystyle 30$	$\displaystyle 30$	$\displaystyle 42$
$\displaystyle 30$-$\displaystyle 40$	\(\displaystyle x\)	\(\displaystyle 42+x\)
$\displaystyle 40$-$\displaystyle 50$	$\displaystyle 65$	\(\displaystyle 107+x\)
$\displaystyle 50$-$\displaystyle 60$	y	\(\displaystyle 107+x+\mathrm{y}\)
$\displaystyle 60$-$\displaystyle 70$	$\displaystyle 25$	\(\displaystyle 132+x+y\)
$\displaystyle 70$-$\displaystyle 80$	$\displaystyle 18$	\(\displaystyle 150+x+\mathrm{y}\)
	$\displaystyle 230$

\[\begin{aligned} & 150+x+y=230 \\ & x+y=80 \end{aligned} \] Median is $\displaystyle 46$ ∴ Median class is $\displaystyle 40$-$\displaystyle 50$ \[46=40+\left[\frac{\dfrac{230}{2}-(42+x)}{65}\right] \times 10 \] On solving, we get \(\displaystyle x=34\) and \(\displaystyle \mathrm{y}=46\)