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 ?

This problem can be solved using the concept of geometric progression.

Step 1: Understand the problem The problem states that one person can spread a rumor to two other people in five minutes. This means that the rumor spreads in a geometric progression, where each "generation" of rumor-spreading is twice as large as the previous one.

Step 2: Set up the geometric progression The geometric progression can be represented as 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, etc., where each term is twice the previous term.

Step 3: Find the term in the progression that represents 729 people We need to find the smallest term in the progression that is greater than or equal to 729. This is the 10th term, which is 1024.

Step 4: Calculate the time Since each term represents 5 minutes of rumor-spreading, the time it takes to spread the rumor to 729 people is 10 terms * 5 minutes/term = 50 minutes.

So, it takes 50 minutes to spread the rumor to 729 people.

This problem is a geometric progression problem. The progression is as follows: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.

Step 1: Identify the pattern The pattern is that each term is double the previous term. This is a geometric progression where the common ratio is 2.

Step 2: Find the term where the number of persons (729) fits in We can see that 729 is not in the sequence. However, 1024 is the first number in the sequence that is larger than 729. This is the 10th term in the sequence.

Step 3: Calculate the time Since it takes 5 minutes to pass the rumor from one person to two other persons, it would take 5 minutes times the term number to pass the rumor to that many people. Therefore, it would take 5 * 10 = 50 minutes to pass the rumor to 1024 people.

However, since we only need to pass the rumor to 729 people, and 729 is between the 9th term (512) and the 10th term (1024), the time it would take to pass the rumor to 729 people is between 45 minutes and 50 minutes.

So, it would take less than 50 minutes to spread the rumor to 729 persons.