For hearing distinct echoes, the minimum distance of the obstacle from the source of sound must be around :

To hear a distinct echo, the time interval between the original and reflected sound must be greater than or equal to 0.1 seconds.

Let us consider the distance between the source of sound and the obstacle as d.

$\therefore$Distance travel by the sound is = d + d = 2d
Time taken = 0.1 s
The speed of sound in air is = 344 m/s
We know that speed  = $\frac{\mathrm{Distance}}{\mathrm{Time}}$

$\Rightarrow$ 344 =$\frac{2\mathrm{d}}{0.1}$

$\Rightarrow$d = $\frac{34.4}{2}$= 17.2 m

Thus, the minimum distance to hear an echo is 17.2 m.

Therefore, we can say that for hearing distinct echoes, the minimum distance of the obstacle from the source of sound must be around 17 m.