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 800 steps to reach every second dustbin. On the other hand, starting from any of the dustbins, it took a maximum 1260 steps to reach every third dustbin.

If Ramesh's one step is 0.77 metre, and the width of the path is negligible, which the following can be the radius of the circular path?

Accepted Answer

D. Let $l$ be the step count distance between consecutive dustbins. Minimum steps to reach every 2nd dustbin is 800 $\implies 2l \ge 800 \implies l \ge 400$. Maximum steps to reach every 3rd dustbin is 1260 $\implies 3l \le 1260 \implies l \le 420$. So $400 \le l \le 420$. Total steps around circumference $C = 5l$. $2000 \le C \le 2100$ steps. In meters: $2000 	imes 0.77 = 1540$ m to $2100 	imes 0.77 = 1617$ m. Circumference $2\pi r \in [1540, 1617]$. $r \in [\frac{1540}{2\pi}, \frac{1617}{2\pi}] = [245.1, 257.35]$ meters. Among the options, 250 metres falls in this range.

Circular Path Radius from Step Counts

Explanation

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