Expected Cat Question

Q1: Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at  a speed of 10 km/hr, reaches B and comes back to A at the same speed. Ram starts at 9:00 am and Shyam starts at 9:45 am from A. Ram reaches B at 10:00 am (as his speed is 5km/hr and the distance between A and B is 5km) When Ram reaches B, Shyam is 15/60 × 10 = 2.5 km away from A. Ram meets Shyam (2.5 × 60)/(10 + 5) minutes after 10:00 a.m. i.e., at 10:10 a.m. Shyam reaches B at 10:15 a.m. At 10:15 a.m., Ram is (15/60) × 5 = 1.25 km away from B. Shyam overtakes Ram in 1.25/(10 – 5) = 0.25 hrs = 15 minutes after 10:15 am i.e. at 10:30 a.m.  Hence Option 2 Q2: Shyam overtakes Ram at 10:30 a.m. Hence, option 2.