xat 2025 Question 11

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

Let's assume that all the dustbins are at equal distances and the distance between two dustbin's be l.

We are told that a minimum 800 steps to reach every second dustbin.

800 $\le$ 2l $\Rightarrow$ 400 $\le$ l

Similarly, we are also told that a maximum 1260 steps to reach every third dustbin.

So, 3l $\le$ 1260 400 $\le$ l $\le$ 420

The circumference will be 5l.

2000 $\le$ 5l $\le$ 2100

2000 and 2100 are both in steps of Ramesh.

We are told that each of his step is 0.77m.

So, 2000 steps = 2000*0.77= 1540m

2100 steps = 2100*0.77 = 1617

So, the circumference will lie between 1540 and 1617.

1540 $\le 2\pi r \le$ 1617.

$\frac{1540}{2\pi}\le r\le\frac{1617}{2\pi}$

$245.22\le r\le\ 257.48$

So, 250m is the correct option.

Question 11.

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