The mean of the following frequency distribution is $\displaystyle 35$ . Find the values of $\displaystyle x$ and $\displaystyle y$, if the sum of frequencies is $\displaystyle 25$ :

lathematics_041_30/$\displaystyle 1$/1_2025-$\displaystyle 26$

Class Interval	Frequency $\displaystyle \left(f_{i}\right)$	$\displaystyle x_{i}$	$\displaystyle f_{i} x_{i}$
$\displaystyle 0$-$\displaystyle 10$	$\displaystyle 1$	$\displaystyle 5$	$\displaystyle 5$
$\displaystyle 10$-$\displaystyle 20$	$\displaystyle x$	$\displaystyle 15$	$\displaystyle 15 x$
$\displaystyle 20$-$\displaystyle 30$	$\displaystyle 5$	$\displaystyle 25$	$\displaystyle 125$
$\displaystyle 30$-$\displaystyle 40$	$\displaystyle 7$	$\displaystyle 35$	$\displaystyle 245$
$\displaystyle 40$-$\displaystyle 50$	$\displaystyle y$	$\displaystyle 45$	$\displaystyle 45 y$
$\displaystyle 50$-$\displaystyle 60$	$\displaystyle 3$	$\displaystyle 55$	$\displaystyle 165$
$\displaystyle 60$-$\displaystyle 70$	$\displaystyle 1$	$\displaystyle 65$	$\displaystyle 65$
Total	$\displaystyle 25$		$\displaystyle 605+15 x+45 y$

\[\sum f_{i}=25 \Rightarrow x+y=8 \] $\displaystyle \operatorname{Mean}(\bar{x})=\frac{605+15 x+45 y}{25}=35$ \[\Rightarrow 15 x+45 y=270 \text { or } x+3 y=18 \]Solving (i) and (ii), we get $\displaystyle x=3, y=5$SECTION - E Question numbers $\displaystyle 36$ to $\displaystyle 38$ are Case Study Based questions, carrying $\displaystyle 4$ marks each