It takes five minutes to pass a rumour from one person to two other persons. The tree of rumour continues. Find how many minutes does it take spread the rumour to 729 persons?

Correct option is C

This problem is like a geometric sequence. If it takes 5 minutes to spread a rumor from one person and every person who hears the rumor tells the next person in 5 minutes, we can see that this is a circular process. It takes 5 minutes to reach from the first person to the second, then it also takes 5 minutes from the second to the third, and so on. We have to see how many levels are needed so that a total of 729 people can hear the rumor. 729 can be written as $$3^6$$​, which means 6 levels are needed. Each level takes 5 minutes. Therefore, the total time will be 5 × 6 = 30 minutes.

Step by Step Solution:
It takes 5 minutes to spread the rumor from the first person to the second person.

To reach 729 people, we have to see how many levels are needed. 729 can be written as $$3^6$$​, i.e. 6 levels.

Step 3
Each level takes 5 minutes, so total time will be 5 × 6 = 30 minutes.