Since, number of observations are even $n=10$

Hence, the median is $=\frac{{\left({\displaystyle \frac{n}{2}}\right)}^{th} term+{\left({\displaystyle \frac{n}{2}}+1\right)}^{th} term}{2}=\frac{5^{th} term+6^{th} term}{2}$

Thus, median $=\frac{34+x}{2}$

$\Rightarrow \frac{34+x}{2}=35$

$\Rightarrow x=36 ...\left(i\right)$

And, mean$=\frac{sum of terms}{number of terms}$

$\Rightarrow \frac{10+22+26+29+34+x+42+67+70+y}{10}=42$

$\Rightarrow x+y+300=420$

$\Rightarrow x+y=120 ...\left(ii\right)$

Put the value of $x$ from $\left(i\right)$ in $\left(ii\right),$ to get

$36+y=120$

$\Rightarrow y=84$

$\Rightarrow \frac{y}{x}=\frac{84}{36}=\frac{7}{3}.$