A class of boys stands in a single line. One particular boy is 19th in order from both the ends of the line. How many boys are there in the class altogether?

Introduction / Context:
This question is about a special case in ranking, where one boy has the same position when counted from both ends of the line. Recognising this pattern allows for a quick calculation of the total number of boys. Such questions often appear in reasoning exams as straightforward applications of the basic rank relationship.

Given Data / Assumptions:

- A single boy is 19th from the left end.- The same boy is also 19th from the right end.- The class forms a single straight line, and there are no ties.

Concept / Approach:
In general, for any person, rank from left + rank from right = total number of persons + 1. Here, both ranks are equal (19th from each end), which makes the calculation especially simple. We can plug the known ranks into the formula and solve for the total number of boys in the line.

Step-by-Step Solution:
Step 1: Let the total number of boys be N.Step 2: The boy's rank from the left is 19.Step 3: The boy's rank from the right is also 19.Step 4: Apply the relation: rank from left + rank from right = N + 1.Step 5: Substitute the values: 19 + 19 = N + 1.Step 6: Compute 19 + 19 = 38, so 38 = N + 1.Step 7: Therefore, N = 38 - 1 = 37.

Verification / Alternative check:
We can interpret the situation visually. If the boy is 19th from both ends, there must be 18 boys on his left and 18 boys on his right. Adding them together with the boy himself gives 18 + 1 + 18 = 37. This intuitive check matches the formula-based answer and confirms that 37 is correct.

Why Other Options Are Wrong:
Option 38 would imply 19 + 19 = 39, which contradicts the rank relationship. Option 39 gives N + 1 = 40, again inconsistent with 19 + 19 = 38. Option 27 is far too small and does not allow for 18 boys on each side of the central boy. Only 37 fits both the formula and the intuitive count from each side.

Common Pitfalls:
A common source of error is misremembering the formula and using N instead of N + 1 on the right-hand side. Some students also forget to include the boy himself when adding those on either side. Carefully applying the correct relation avoids these mistakes.

Final Answer:
The number of boys in the class is 37.