There are n equally spaced points 1,2,...,n marked on the circumference of a circle. If the point 15 is directly opposite to the point 49, then the total number of points is

Given: $n$ equally spaced points $1, 2, \ldots, n$ marked on circumference of a circle
Point $15$ is directly opposite to point $49$
Since the points are equally spaced on a circle, two points are directly opposite if they are diametrically opposite
$\therefore$ The number of points between $15$ and $49$ on each semicircle must be equal
Points between $15$ and $49$ (going from $15$ to $49$):
$16, 17, 18, \ldots, 48$
Number of points $= 48 - 16 + 1 = 33$
Since both semicircles must have equal number of points between the opposite points:
Points on other semicircle (from $49$ to $15$) must also be $33$
$\therefore$ Total number of points $= 2 + 33 + 33 = 68$