Question

In a row of boys, Akhil is 13th from beginning and Bharat is 14th from the end of row. There are 6 boys in between them. If 2 boys from the beginning and 3 boys from the end of row left, what is the new position of Akhil from the end of row ?

• A. 17th
• B. 18th
• C. 16th
• D. 19th

Hint:

Be careful when boys leave from the end of the row.
Since Akhil is positioned towards the start, boys leaving from the end do not change his position from the start, but they do reduce the total count, which shifts his position relative to the end.
Always calculate the new total first to avoid indexing errors.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This is a ranking and order problem.
We are given the positions of two boys (Akhil and Bharat) from opposite ends of a row and the number of boys between them.
After some boys leave from both ends, the row is altered, and we need to calculate Akhil's new position from the end of the row.

Step 2: Key Formula or Approach:
The total number of boys $N$ in a non-overlapping scenario is:
\[ N = \text{Position from start} + \text{Number of boys in between} + \text{Position from end} \] When a person's position from the beginning is $P_{\text{beg}}$, their position from the end $P_{\text{end}}$ in a row of total $T$ people is:
\[ P_{\text{end}} = T - P_{\text{beg}} + 1 \]

Step 3: Detailed Explanation:

• Calculate the Initial Total Number of Boys ($N$):
Given:
- Akhil's position from start $= 13$
- Bharat's position from end $= 14$
- Boys in between $= 6$
Since it is a standard non-overlapping case:
\[ N = 13 + 6 + 14 = 33 \text{ boys} \]

• Analyze the Changes in the Row:
- "2 boys from the beginning left":
Since 2 boys left from the start, Akhil's new position from the beginning becomes:
\[ P_{\text{beg}} = 13 - 2 = 11\text{th} \]
- "3 boys from the end left":
A total of $2$ boys from the start and $3$ boys from the end left.
The new total number of boys ($T$) in the row is:
\[ T = 33 - 2 - 3 = 28 \text{ boys} \]

• Calculate Akhil's New Position from the End:
Using the position formula:
\[ P_{\text{end}} = T - P_{\text{beg}} + 1 \] \[ P_{\text{end}} = 28 - 11 + 1 = 17 + 1 = 18\text{th} \]

Step 4: Final Answer:
The new position of Akhil from the end of the row is 18th.
Therefore, the correct option is (B).