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 question is a classic example of weighted averages and mixture of groups. It tests the ability to combine average values when two groups with different sizes and different averages are merged.

Given Data / Assumptions:
- Initial average age of the group = 16 years.
- Number of initial members = n (unknown).
- 20 new persons join later.
- Average age of the 20 new persons = 15 years.
- Final average of the combined group = 15.5 years.
- All ages are in years.

Concept / Approach:
We use the relationship:
Total age = Average age * Number of persons
Initially and after new persons join. We set up an equation based on the total age of the original group plus the total age of the new members equalling the total age implied by the final average.

Step-by-Step Solution:
Step 1: Let the original number of persons be n.Step 2: Initial total age = 16 * n.Step 3: Total age of the 20 new persons = 15 * 20 = 300.Step 4: Final total number of persons = n + 20.Step 5: Final total age from the final average = 15.5 * (n + 20).Step 6: Set up equation: 16n + 300 = 15.5 * (n + 20).Step 7: Expand the right side: 16n + 300 = 15.5n + 310.Step 8: Rearrange: 16n - 15.5n = 310 - 300, so 0.5n = 10.Step 9: Solve for n: n = 10 / 0.5 = 20.

Verification / Alternative check:
Original total age = 16 * 20 = 320. New persons total age = 300. Combined total age = 320 + 300 = 620. Combined number of persons = 20 + 20 = 40. Combined average = 620 / 40 = 15.5 years, which matches the given final average, confirming that the original group size is correct.

Why Other Options Are Wrong:
- 15, 23 and 24 do not satisfy the equation when substituted for n and would give a combined average different from 15.5 years.
- For example, if n were 15, the total age would be 240 + 300 = 540, with 35 persons, giving an average of about 15.43, not 15.5.

Common Pitfalls:
- Adding the averages directly instead of working with total ages.
- Forgetting that the number of persons changes when 20 new persons join, so the divisor in the average must be n + 20, not just n.
- Mixing up which average applies to which group.

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