Question

In a game of musical chairs, 16 girls are participating. Every round of music will have 2 minutes duration. An interval of 5 minutes is given after every 5 rounds of music. How much time will it take to complete the game?
(a) 47 min
(b) 45 min
(c) 35 min
(d) 40 min

Answer 1

Hint: To solve the given question, we will first find out what the rules of the game of musical chairs are. Then, we will find out what will be the total number of rounds required to complete the game if the number of participants is 16. Then we will multiply the total number of rounds by 2 to get total rounds duration. Then, on the basis of the total number of rounds, we will determine how many intervals will be there considering that there is an interval after every five rounds and we will add 5 minutes for every interval in the total round duration to get the total game time.

Complete step by step answer:
In the game of musical chairs, if there are no participants (n – 1) chairs are taken initially and as soon as the music stops, the participants have to quickly sit on these chairs. The one which couldn’t sit is eliminated. Now, one chair is removed and the same process is repeated and one more participant is eliminated. This process is repeated until there is only one chair left and two participants left. The one who sits on that chair is the winner. If the total participants are n, then we can say that there will be (n – 1) rounds. Thus, in our case, we have 16 girls as participants so there will be 15 rounds.
Now, it is given in the question that each round requires two minutes. So, 15 rounds will take \[15\times 2\text{minutes}=30\text{ minutes}\text{.}\]
Thus, the total round duration = 30 minutes.
Now, after every 5 rounds, there is an interval of 5 minutes. In our case, after 5 rounds, there will be the first interval, after the next 5 rounds, there will be the second interval and then we have the last 5 rounds. So, there are a total of 2 intervals. Now, the duration of each interval is 5 minutes. So, the total interval duration will be equal to the interval duration of two intervals. Thus,
Total Interval Duration = 2 \[\times \] interval duration of one interval
Total Interval Duration = 10 minutes
Now, the total game time will be the sum of the round duration and total interval duration. Thus, we have,
Total Game Time = 30 minutes + 10 minutes
Total game time = 40 minutes
Hence, option (d) is the right answer.

Note: The shortcut method to find the total interval duration is given by the formula shown below. If there are n rounds and t is the interval duration of one interval and the interval happens after every r round then the total interval duration will be,
\[\text{Total Interval Duration}=\left[ \dfrac{n-1}{r} \right]t\]
In our case, n = 15, r = 5 and t = 5. Thus, we have,
\[\Rightarrow \text{Total Interval Duration}=\left[ \dfrac{15-1}{5} \right]\times 5\]
\[\Rightarrow \text{Total Interval Duration}=\left[ \dfrac{14}{5} \right]\times 5\]
\[\Rightarrow \text{Total Interval Duration}=\left[ 2.8 \right]\times 5\]
\[\Rightarrow \text{Total Interval Duration}=2\times 5\]
Therefore, the total interval duration = 10 minutes.