In a row of thirty boys, R is fourth from the right end and W is tenth from the left end. How many boys are there between R and W in the row?

Introduction / Context:
Row arrangement and ranking questions require you to translate positions from right and left ends into absolute positions and then measure distances between them. In this question, you know the total number of boys in the row and the positions of R and W from opposite ends. The task is to find how many boys are seated strictly between them.

Given Data / Assumptions:
- Total number of boys in the row = 30. - R is fourth from the right end. - W is tenth from the left end. - All positions in the row are occupied by distinct boys.

Concept / Approach:
To compare positions from different ends, you first convert them to positions from a common side, usually from the left. If the total number of boys is N, then a position that is k-th from the right is at (N - k + 1) from the left. Once both positions are expressed from the same side, subtract the smaller from the larger and reduce by one to get the count of boys in between. This approach is standard for many exam questions of this type.

Step-by-Step Solution:
Step 1: Total number of boys N = 30. Step 2: R is fourth from the right. So his position from the left is N - 4 + 1 = 30 - 4 + 1 = 27. Step 3: W is tenth from the left, so W is at position 10 from the left. Step 4: We now have R at position 27 and W at position 10 when counted from the left. Step 5: To find how many boys sit between them, compute the difference between their positions and subtract 1. Step 6: Difference between 27 and 10 is 27 - 10 = 17. Step 7: The number of boys between R and W = 17 - 1 = 16.

Verification / Alternative check:
Imagine the row indexed from the left: positions 1 to 30. W sits at position 10. R sits at position 27. If you count from 11 up to 26, you get the boys between them. The number of such positions is 26 - 11 + 1, which equals 16. This matches the earlier calculation and verifies the result without relying solely on formulas.

Why Other Options Are Wrong:
15: This would be correct if the positions differed by 16, which they do not. 17: This incorrectly takes the full difference between the positions without subtracting one for the endpoints. Cannot be determined: The total number of boys and both positions are given clearly, so the answer is uniquely determined.

Common Pitfalls:
A common error is forgetting to subtract one after taking the difference of positions. This leads to counting one of the end boys as being between themselves, which is not correct. Another mistake is miscalculating the left side position from the right side position by using N - k instead of N - k + 1. Writing out the positions and verifying them visually can prevent such slips in competitive exam settings.

Final Answer:
The number of boys sitting between R and W in the row is 16.