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:

A. 30 km/h

B. 25 km/h

C. 20 km/h

D. 35 km/h

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & x + y = 70 \cr & \frac{{30}}{x} + \frac{{30}}{y} = \frac{{21}}{{10}} \cr & 30\left[ {\frac{{x + y}}{{xy}}} \right] = \frac{{21}}{{10}} \cr & \frac{{30 \times 70}}{{xy}} = \frac{{21}}{{10}} \cr & xy = 1000 \cr & {\left( {x - y} \right)^2} = {\left( {x + y} \right)^2} - 4xy \cr & {\left( {x - y} \right)^2} = 4900 - 4000 \cr & {\left( {x - y} \right)^2} = 900 \cr & \left( {x - y} \right) = 30\,{\text{km/hr}} \cr} $$