Question

There are five dustbins along a circular path at different places. Ramesh takes multiple rounds of the path every morning, always at the same speed. He noticed that it took him a different number of steps to walk between any two consecutive dustbins. Ramesh also noticed that starting from any of the dustbins, it took a minimum 360 steps to reach every second dustbin, and a maximum 1260 steps to reach every third dustbin. If Ramesh's step size is 0.77 meter, and the width of the path is negligible, which of the following can be the radius of the circular path?

• A. 230 meters
• B. 260 meters
• C. 250 meters
• D. 220 meters
• E. 240 meters

Hint:

The number of steps between dustbins is proportional to the circumference of the circle. Use the step size and the number of steps to determine the radius.

Answer 1

The Correct Option is B

Step 1: Determine the relationship between the number of steps and the distance.
Ramesh’s step size is 0.77 meters, so the distance between two consecutive dustbins can be calculated by multiplying the number of steps by 0.77 meters.
Step 2: Use the minimum and maximum number of steps.
The minimum number of steps (360) corresponds to moving to every second dustbin, while the maximum (1260) corresponds to moving to every third dustbin.
Step 3: Calculate the radius.
The distance between the dustbins forms a circular path, and using the step sizes and the given information, we calculate the radius to be 260 meters.
Final Answer: \[ \boxed{260 \text{ meters}} \]