Aptitude 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 $n$

**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 $N=\textbf{7}$