Define variables

Let Ravi's speed be $x$ km/hr and Ram's speed be $y$ km/hr. Time taken by Ravi is $T_{\text{Ravi}} = 20/x$ and by Ram is $T_{\text{Ram}} = 20/y$.

$T_{\text{Ravi}} = \frac{20}{x}, T_{\text{Ram}} = \frac{20}{y}$

Set up time equations

From the first condition: $T_{\text{Ram}} = T_{\text{Ravi}} + 2$. From the second condition: $T_{\text{Ravi}} = T_{\text{Ram}'} + 4/3$, where $T_{\text{Ram}'}$ is time when speed is $2y$, so $T_{\text{Ram}'} = 20/(2y) = 10/y$.

$\frac{20}{y} = \frac{20}{x} + 2, \quad \frac{20}{x} = \frac{10}{y} + \frac{4}{3}$

Solve the system

Substitute $20/y = 20/x + 2$ into the second equation: $20/x = (20/y)/2 + 4/3 = 10/y + 4/3$. We have $10/y = 10/x + 1$ (dividing first by 2). Substituting $10/y$ into the second: $20/x = (10/x + 1) + 4/3$. Rearranging gives $10/x = 7/3$, so $x = 30/7 = 4 \frac{2}{7}$.

$x = \frac{30}{7} = 4\frac{2}{7}$