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

Since, N persons are standing on the circumference of a circle at distinct points and each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other.

Total time taken is 28 minutes when each pair sings for 2 minutes, then total time taken will be 14 minutes when each pair sings for 1 minute. 

A person standing can't form pair with himself and with his two neighbours. Hence, total possible pairs = N * (N - 3).

This also includes the pair in both clockwise and anticlockwise direction. 

Hence, the actual number of pair = $$\frac{[N(N - 3)]}{2} = 14$$

N(N - 3)=28

N = 7