Question

Two straight roads R1 and R2 diverge from a point A at an angle of 120°. Ram starts walking from point A along R1 at a uniform speed of 3 km/hr. Shyam starts walking at the same time from A along R2 at a uniform speed of 2 km/hr. They continue walking for 4 hr along their respective roads and reach points B and C on R1 and R2 respectively. There is a straight line connecting B and C. Then Ram returns to point A after walking along the line segments BC and CA. Shyam also returns to A after walking along line segments BC and CA. Their speeds remain unchanged. The time interval (in hours) between Ram's and Shyam's return to the point A is:

• A. $\frac{10\sqrt{19} + 26}{3}$
• B. $\frac{2\sqrt{19} + 10}{3}$
• C. $\frac{\sqrt{19} + 26}{3}$
• D. $\frac{\sqrt{19} + 10}{3}$

Hint:

When dealing with travel problems involving multiple paths and return times, use geometry and the law of cosines to compute the necessary distances and times.

Answer 1

The Correct Option is A

Ram and Shyam walk along different paths, and their total distance and travel times can be computed by considering the geometry of the situation. Using the law of cosines and distances, we compute the time taken by both Ram and Shyam to return to point A, and the difference in the times taken. The time interval between Ram's and Shyam's return to point A is given by: \[ \frac{10\sqrt{19} + 26}{3} \]