In a row of boys, Rajan is sixth from the left end and Vinay is tenth from the right end. If there are exactly eight boys sitting between Rajan and Vinay, how many boys are there in the row in total?

Introduction / Context:
This problem is a typical row ranking question involving positions from the left and from the right, along with a known number of persons between two given persons. Such questions are very common in competitive examinations and are designed to test the ability to combine different forms of positional information to find the total number of persons in the row.

Given Data / Assumptions:

• All persons are boys sitting in a straight row.
• Rajan is 6th from the left end of the row.
• Vinay is 10th from the right end of the row.
• There are exactly 8 boys sitting between Rajan and Vinay.
• No other special conditions are given, and both boys are part of the same continuous row.

Concept / Approach:
For such questions, the standard formula when two persons are in a row with a known number of persons between them is: total number of persons = position of first person from one end + position of second person from the other end + number of persons between them.
This works when the two persons are distinct and the positions are counted from opposite ends of the same row. The formula effectively accounts for the segments of the row on both sides and in between the two persons.

Step-by-Step Solution:
Step 1: Note that Rajan is 6th from the left. Step 2: Vinay is 10th from the right. Step 3: The number of boys between them is 8. Step 4: Apply the standard formula for total number of boys in the row. Step 5: Total boys = 6 (Rajan from left) + 10 (Vinay from right) + 8 (between them). Step 6: Total boys = 6 + 10 + 8 = 24. Step 7: Therefore, there are 24 boys in the row.

Verification / Alternative check:
Imagine the row as a line of 24 positions. Rajan at 6th from left means his position is 6. Vinay at 10th from right in a row of 24 means his position from left is 24 - 10 + 1 = 15. The number of boys between positions 6 and 15 is 15 - 6 - 1 = 8, which matches the given condition, so the total of 24 is consistent and correct.

Why Other Options Are Wrong:
Option 26 gives too many positions and would increase the number of boys between Rajan and Vinay beyond 8. Option 23 or 25 both break the relation between the given ranks and the stated number of boys between them.

Common Pitfalls:
Many students incorrectly add only one of the ranks to the number of students between or forget that ranks from opposite sides both include the persons themselves. Using the standard formula avoids forgetting to include any segment of the row and keeps the calculation straightforward.

Final Answer:
There are 24 boys in the row in total.