In a row of 15 children, when Raju is shifted three places towards the right, he becomes 8th from the right end. What was his original position from the left end of the row before he moved?

Introduction / Context:
This is a classic ranking and arrangement problem that often appears in reasoning tests. The problem describes a row of children and gives Raju’s position from the right after he has moved three places to the right. The task is to determine his original position from the left. Solving such problems requires understanding how left and right positions are related when the total number in the row is known.

Given Data / Assumptions:

• The total number of children in the row is 15.
• After moving three places to the right, Raju becomes 8th from the right end.
• Before moving, he was three places to the left of his new position.
• Positions from the left and positions from the right are counted starting at 1.
• We assume that no other child changes position during Raju’s movement.

Concept / Approach:
There are two key ideas. First, for a line of N people, the relationship between a person’s position from the left and from the right is: left position + right position - 1 = N. Second, when Raju moves three places to the right, his position from the left increases by 3. If we find his new position from the left and subtract 3, we obtain his original position from the left.

Step-by-Step Solution:
Step 1: Use the relationship between left and right positions. For a total of 15 children, left position + right position - 1 = 15.Step 2: After the move, Raju is 8th from the right. Let his new position from the left be L_new.Step 3: Apply the formula: L_new + 8 - 1 = 15.Step 4: Simplify: L_new + 7 = 15, so L_new = 15 - 7 = 8.Step 5: So after the movement, Raju is 8th from the left as well as 8th from the right.Step 6: Raju originally was three places to the left of this new position, so his original left position L_original = L_new - 3.Step 7: Compute L_original = 8 - 3 = 5.Step 8: Therefore Raju was originally 5th from the left end of the row.

Verification / Alternative check:
We can visualize the row briefly. With 15 children, the positions from the left are numbered 1 through 15, and from the right they are 15 through 1. If Raju is now 8th from the right, he is at the position that matches left position 8. If he moved three places to the right to reach position 8, then he must have been at position 5 earlier. This simple visual line check is consistent with the algebraic solution.

Why Other Options Are Wrong:
If Raju had originally been at position 14 or 12 from the left, moving three places to the right would place him beyond the end of the row, which is impossible. If he had been 6th from the left, moving three places to the right would make him 9th from the left, which would correspond to 7th from the right in a row of 15, not 8th. Therefore these options do not match the given information.

Common Pitfalls:
Some learners mistakenly add or subtract positions from the wrong side or forget to use the total number in the row when relating left and right positions. Others forget that moving to the right increases the left position number. Keeping the relationship left position + right position - 1 = total can help avoid these errors.

Final Answer:
Raju’s original position from the left end of the row was 5.