Rahul and Mithun travel a distance of 30 km. The sum of their speeds is 70 km/h and the total time taken by both to travel the distance is 2 hours 6 minutes. The difference between their speeds is:

Let the speed of Rahul = s

$$\Rightarrow$$ Speed of Mithun = 70 - s

Time taken by Rahul to cover 30 km distance = $$\frac{30}{s}$$

Time taken by Mithun to cover 30 km distance = $$\frac{30}{70-s}$$

Given, total time = 2 hours 6 minutes = 2 + $$\frac{6}{60}$$ hours = 2 + $$\frac{1}{10}$$ hours = $$\frac{21}{10}$$ hours

$$\Rightarrow$$  $$\frac{30}{s}+\frac{30}{70-s}=\frac{21}{10}$$

$$\Rightarrow$$  $$\frac{1}{s}+\frac{1}{70-s}=\frac{7}{100}$$

$$\Rightarrow$$  $$\frac{70-s+s}{s\left(70-s\right)}=\frac{7}{100}$$

$$\Rightarrow$$  $$\frac{70}{70s-s^2}=\frac{7}{100}$$

$$\Rightarrow$$  $$70s-s^2=1000$$

$$\Rightarrow$$  $$s^2-70s+1000=0$$

$$\Rightarrow$$  $$s^2-50s-20s+1000=0$$

$$\Rightarrow$$  $$s\left(s-50\right)-20\left(s-50\right)=0$$

$$\Rightarrow$$  $$\left(s-50\right)\left(s-20\right)=0$$

$$\Rightarrow$$  $$s-50=0$$   or   $$s-20=0$$

$$\Rightarrow$$  s = 50 km/h or   s = 20 km/h

When speed of Rahul = 50 km/h, speed of mithun = 20 km/h

When speed of Rahul = 20 km/h, speed of mithun = 50 km/h

$$\therefore\ $$Difference between their speeds = 30 km/h

Hence, the correct answer is Option D