The average age of a group of persons going for a picnic is 16 years. On the spot, 20 new persons with an average age of 15 years join the group, and the overall average age becomes 15.5 years. How many persons were there in the original picnic group?

Introduction / Context:
This is a classic mixture of averages problem where two groups with different average ages combine to form a larger group with a new average age. These types of questions appear widely in aptitude exams to test how well you handle the relationship between totals and averages when groups merge or split.

Given Data / Assumptions:

Initial group has an average age of 16 years.
Let the number of persons in the initial group be n.
On the spot, 20 new persons join, and these new persons have an average age of 15 years.
After joining, the combined average age becomes 15.5 years.
We need to find the original number of persons n in the picnic group.

Concept / Approach:
We treat the initial group and the new group as two sets with their own totals. The initial total age is 16 * n. The total age of the 20 new persons is 15 * 20. When they combine, the total number of persons is n + 20, and the total age is the sum of the two totals. The new combined average is 15.5, so total combined age = 15.5 * (n + 20). Setting the sum of the two group totals equal to this combined total yields an equation in n that we can solve.

Step-by-Step Solution:
Step 1: Express the total ages of the two groups. Initial total age = 16 * n. Total age of new 20 persons = 15 * 20 = 300. Step 2: Express the combined total age using the final average. Combined number of persons = n + 20. Combined total age = 15.5 * (n + 20). Step 3: Set up the equation. Initial total + new total = combined total. So, 16n + 300 = 15.5 * (n + 20). Step 4: Solve the equation for n. Expand the right side: 15.5 * (n + 20) = 15.5n + 310. So, 16n + 300 = 15.5n + 310. Bring terms involving n to one side: 16n - 15.5n = 310 - 300. 0.5n = 10, hence n = 10 / 0.5 = 20.

Verification / Alternative Check:
If the original group has 20 persons with average age 16, their total age is 20 * 16 = 320. The new 20 persons have total age 300. Combined total age = 320 + 300 = 620, and combined number of persons = 40. The combined average is 620 / 40 = 15.5 years, which matches the given final average, confirming that n = 20 is correct.

Why Other Options Are Wrong:
Option 15 would give an initial total of 240, leading to a different combined average not equal to 15.5 years.
Option 23 or 24 similarly produce totals that do not result in the final average of 15.5 years when combined with the new group of 20 persons with average age 15 years.

Common Pitfalls:
A common mistake is to simply average 16 and 15 to get 15.5 and assume the groups are equal in size without checking the actual numbers. Another error is mishandling the algebraic equation, especially when multiplying the decimal 15.5. Some candidates also misinterpret the question and try to find the final number of persons instead of the original group size.

Final Answer:
The number of persons initially going for the picnic is 20.