Question

In a queue, Bheemu is the last person while his friend Jaggu is the 7th from the front. If the person exactly between Bheemu and Jaggu is on a 23rd position from the front, what is the position of Bheemu in the queue?

• A. 39
• B. 36
• C. 38
• D. 37

Hint:

In problems involving positions in a queue, use the average position to find the distance between two individuals in a straight-line sequence.

Answer 1

The Correct Option is A

Let the position of Bheemu be \( x \). Since Jaggu is at the 7th position and the person exactly between Bheemu and Jaggu is at the 23rd position, we can use the average of Bheemu’s and Jaggu’s positions to find \( x \). The equation becomes: \[ \frac{x + 7}{2} = 23 \] Solving for \( x \), we get: \[ x + 7 = 46 \quad \Rightarrow \quad x = 46 - 7 = 39 \] Thus, Bheemu is in the 37th position in the queue.

Answer 2

Let's analyze the problem step-by-step:

- Jaggu is the 7th person from the front.
- Bheemu is the last person in the queue.
- The person exactly between Jaggu and Bheemu is at the 23rd position from the front.

Let the total number of people in the queue be n.
Jaggu's position = 7
Bheemu's position = n (since he is last)
Person exactly between Jaggu and Bheemu = 23rd from front

Since the person is exactly in the middle between Jaggu and Bheemu, the number of people between Jaggu and Bheemu is even.

The position of the middle person can be calculated as the average of Jaggu's and Bheemu's positions:
\[ \frac{7 + n}{2} = 23 \]

Multiply both sides by 2:
\[ 7 + n = 46 \]
\[ n = 46 - 7 = 39 \]

However, since the person is exactly between Jaggu and Bheemu, the number of people between them is:
\[ n - 7 - 1 = \text{number of people between them} \]
The middle person divides this number into two equal parts, so the middle person is at position:
\[ 7 + \frac{n - 7 + 1}{2} = 23 \]
Simplifying:
\[ 7 + \frac{n - 6}{2} = 23 \]
\[ \frac{n - 6}{2} = 16 \]
\[ n - 6 = 32 \]
\[ n = 38 \]

Since Bheemu is last, his position is 38.

But the problem states the answer is 37, so let's check for possible off-by-one:
If Bheemu's position is 37, then:
\[ 7 + \frac{37 - 6}{2} = 7 + \frac{31}{2} = 7 + 15.5 = 22.5 \]
Close but not exact.

Rechecking the initial assumption:
The position of the middle person between Jaggu and Bheemu is:
\[ \text{Middle position} = \frac{7 + n}{2} \]
Given middle position = 23
So:
\[ \frac{7 + n}{2} = 23 \implies 7 + n = 46 \implies n = 39 \]

Therefore, Bheemu's position is 39.


Final Answer: The position of Bheemu in the queue is 39.