In a geometric spreading process, a secret can be told by one person to only 3 other persons in 3 minutes, and in each subsequent 3-minute interval every person who already knows the secret tells it to 3 new persons only once in the next interval. In a total time of 30 minutes, how many persons (excluding the original person) will have been told this secret in this way?

Introduction / Context:
This question tests exponential growth and geometric progression in a word problem setting. A secret spreads from person to person, and each person passes the secret to a fixed number of new persons in fixed time intervals. Many aptitude tests use this type of problem to check whether candidates understand repeated multiplication rather than simple addition. The twist here is that every person tells the secret to exactly 3 new persons only once, during the 3-minute interval immediately after they first learn the secret. We must carefully track how many new people are informed during each 3-minute block over a total of 30 minutes and then exclude the original person from the final count.

Given Data / Assumptions:
- One original person initially knows the secret.
- In the first 3 minutes, that person tells the secret to 3 new persons.
- In every subsequent 3-minute interval, each person who already knows the secret tells it to exactly 3 new persons only once in the following interval.
- Total time is 30 minutes, which equals 10 intervals of 3 minutes each.
- We must count all persons who have been told the secret, excluding the original person.

Concept / Approach:
The number of people who learn the secret in each interval follows a geometric progression with common ratio 3. In interval 1, there are 3 new people. In interval 2, the 3 new people from interval 1 each tell 3 new people, giving 3^2 new people, and so on. After n intervals, the number of new people in interval n is 3^n. The cumulative number of people who have been told (excluding the original person) is the sum of this geometric series from n = 1 to n = 10.

Step-by-Step Solution:
Interval length = 3 minutes, total time = 30 minutes, so number of intervals = 30 / 3 = 10. New people told in interval 1 = 3^1 = 3. New people told in interval 2 = 3^2 = 9. Generally, in interval n, new people told = 3^n. Total people told (excluding original) = 3^1 + 3^2 + ... + 3^10. This is a geometric series: sum = 3 * (3^10 - 1) / (3 - 1). Compute 3^10 = 59049, so sum = 3 * (59049 - 1) / 2 = 3 * 59048 / 2. 3 * 59048 = 177144; divide by 2 gives 88572. We already excluded the original person in this sum, so the answer is 88572.

Verification / Alternative check:
We can quickly check reasonableness by approximating growth. Numbers progress as 3, 9, 27, 81, 243 and so on, reaching tens of thousands by the tenth step. Therefore, an answer in the range of about 80,000–100,000 is reasonable. 88572 fits this scale and matches the exact formula for the geometric sum, so the value is consistent both algebraically and intuitively.

Why Other Options Are Wrong:
Option 77854 is lower than the correct geometric sum and does not match any standard partial sum for 10 intervals.
Option 99584 is higher than the correct value 88572 and again does not correspond to the geometric series sum.
Option 55654 is far from the correct total and is likely included as a distractor that might come from arithmetic errors in summation.

Common Pitfalls:
A common mistake is to treat the process as simple addition, for example adding 3 every interval instead of allowing each informed person to tell 3 more people. Another frequent error is to assume each person continues to tell the secret in every interval, which would lead to a different and much larger progression. Some candidates also forget that the question asks for the count excluding the original person, but in our series we never included that person in the sum, so the issue is avoided.

Final Answer:
Thus, the number of persons who have been told the secret, excluding the original person, is 88572.