# Moderate Algebra Solved QuestionAptitude Discussion

 Q. $N$ 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 $N$?
 ✖ A. 5 ✔ B. 7 ✖ C. 9 ✖ D. 4

Solution:
Option(B) is correct

Each person will form a pair with all other persons except the two beside him. Hence he will form $(n–3)$ pairs.

If we consider each person, total pairs $=n(n–3)$ but here each pair is counted twice.

Hence actual number of pairs

$=\dfrac{n(n-3)}{2}$

They will sing for

$=\dfrac{n(n-3)}{2}\times 2$

$=n(n-3)=28$

$\Rightarrow n=7$

Hence, n= 7 by discarding -ve value of $n$

## (1) Comment(s)

Prakash
()

The solution can be explained in a different manner as follows: Each person will form a pair with $(N-3)$ persons(as we have to exclude the two person on either side.

So the total no. pairs formed $\dfrac{N \times (N-3)}{2}$ and they will sing for $\dfrac{N(N-3)}{2}\times2$ minutes (since each pair sings for two minutes)

The total singing time is 28 min..

So $N\times (N-3)=28$

which gives $N=\textbf{7}$