The time required for a boy to travel along the external and internal boundaries of a circular path are in the ratio 20:19. If the width of the path be 5 metres, the internal diameter is :
1). 195 metres
2). 192 metres
3). 180 metres
4). 190 metres
Let internal radius of the path be $r$ m and thus external radius $= (r+5)$ m
As, distance $\propto$ time
$= \frac{2\pi (r+5)}{2\pi r}=\frac{20}{19}$
$= 19r+95=20r$
$= 20r-19r=r=95$
$\therefore$ Internal diameter $= 2\times95=190$ m
= Ans Option (4) - $190$ meter