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: Establish the relationship between step count and distance.
Ramesh’s step length is 0.77 meters; therefore, the distance between adjacent dustbins is determined by multiplying the number of steps by 0.77 meters.
Step 2: Utilize the minimum and maximum step counts.
The minimum step count (360) represents travel to every second dustbin, and the maximum step count (1260) represents travel to every third dustbin.
Step 3: Compute the radius.
The distances between dustbins form a circular route. Based on the step lengths and provided data, the calculated radius is 260 meters.
Final Answer: \[\boxed{260 \text{ meters}}\]