N
persons stand on the circumference of a circle at distinct points. Each
possible pair of persons, not standing next to each other, sings a two-minute
song one pair after the other. If the total time taken for singing is 28
minutes, what is N?

Total
number of pairs is N C 2.

Number
of pairs standing next to each other = N.

Therefore,
number of pairs in question = N C 2- N = 28/2 = 14.