IIM-K (BMSAT) 2025 (QA) PYQs

Two swimmers, Ankit and Bipul, start swimming from the opposite ends of a swimming pool at the same time. Ankit can cover the length of the pool once in 10 minutes. Bipul can cover the length of the pool once in 15 minutes. They swim back and forth for 80 minutes without stopping. The number of times they meet each other is

Vinita drives a car which has four gears. The speed of the car in the fourth gear is five times its speed in the first gear. The car takes twice the time to travel a certain distance in the second gear as compared to the third gear. In a 100 km journey, if Vinita travels equal distances in each of the gears, she takes 585 minutes to complete the journey. Instead, if the distances covered in the first, second, third, and fourth gears are 4 km, 4 km, 32 km, and 60 km, respectively, then the total time taken, in minutes, to complete the journey, will be

Ram and Shyam run a race between points $A$ and $B, 5 \mathrm{~km}$ apart. Ram starts at 9 AM from $A$ at a speed of $5 \mathrm{~km} / \mathrm{hr}$, reaches $B$ and returns to $A$ at the same speed. Shyam starts at $9: 45 \mathrm{AM}$ from $\mathrm{A}$ at a speed of $10 \mathrm{~km} / \mathrm{hr}$, reaches $B$ and comes back to $A$ at the same speed.

At what time does Shyam overtake Ram ?