Step 1: Write the cumulative frequency table.

| Class | $f$ | c.f. |
|---|---|---|
| 65 - 85 | 4 | 4 |
| 85 - 105 | 5 | 9 |
| 105 - 125 | $x$ | $9 + x$ |
| 125 - 145 | 20 | $29 + x$ |
| 145 - 165 | 14 | $43 + x$ |
| 165 - 185 | $y$ | $43 + x + y$ |
| 185 - 205 | 4 | $47 + x + y$ |

Step 2: Total frequency $= 68$.
$$47 + x + y = 68 \Rightarrow x + y = 21 \qquad \ldots (i)$$
Step 3: Median $= 137$ lies in the class $125 - 145$ (median class).
So $l = 125$, $f = 20$, $h = 20$, $cf = 9 + x$, $\dfrac{n}{2} = \dfrac{68}{2} = 34$.
Step 4: Apply the median formula.
$$\text{Median} = l + \left(\frac{\frac{n}{2} - cf}{f}\right) \times h$$
Step 5: $$137 = 125 + \left(\frac{34 - (9 + x)}{20}\right) \times 20$$
$$137 - 125 = 34 - 9 - x \Rightarrow 12 = 25 - x$$
Step 6: $$x = 13$$
Step 7: From $(i)$ : $$y = 21 - 13 = 8$$
Hence $x = 13$ and $y = 8$.