1. Use the median condition

The 10 numbers are already arranged in increasing order:

$10,\ 22,\ 26,\ 29,\ 34,\ x,\ 42,\ 67,\ 70,\ y$

For 10 observations, the median is the average of the 5th and 6th terms.

So,

$\text{Median} = \frac{34+x}{2} = 35$

Thus,

$34+x=70$ $x=36$

2. Use the mean condition

Mean of the 10 numbers is 42, so their total sum is:

$10\times 42 = 420$

Now sum the known terms:

$10+22+26+29+34+36+42+67+70+y = 420$

First add the constants:

$10+22=32$ $32+26=58$ $58+29=87$ $87+34=121$ $121+36=157$ $157+42=199$ $199+67=266$ $266+70=336$

So,

$336+y=420$ $y=84$

3. Compute $\dfrac{y}{x}$

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

4. Match with the options

$\frac{y}{x}=\frac{7}{3}$

So the correct option is D.