In a row of buses, the Panjab bus stands at the 19th position from the right end. The Raftaar bus is 23 places to the left of the Panjab bus and is exactly at the centre of the row. How many buses are standing strictly between the Raftaar bus and the bus at the extreme left end of the row?

Introduction / Context:
This is a typical ranking and arrangement question involving positions of buses in a single row. The goal is to translate the verbal description into positions counted from one end, find the total number of buses and then compute how many buses lie between two specific positions in the row.

Given Data / Assumptions:

• Panjab bus is 19th from the right end.
• Raftaar bus is 23 places to the left of the Panjab bus.
• Raftaar bus is exactly at the centre of the row.
• All buses are arranged in a straight line, and positions are counted in whole numbers.

Concept / Approach:
We use two key ideas:

• Relationship between rank from left and rank from right when total number of items is known.
• The central position in a row of N buses (where N is odd) is (N + 1) / 2 from either end.

We form equations using the information about the centre and the relative distances between the buses to find the total number of buses and then count the buses between two positions.

Step-by-Step Solution:
Step 1: Let the total number of buses be N. Step 2: Panjab is 19th from the right. From the left, its position = N - 19 + 1 = N - 18. Step 3: Raftaar is 23 places to the left of Panjab, so Raftaar's position from the left = (N - 18) - 23 = N - 41. Step 4: We are told that the Raftaar bus is exactly at the centre of the row. For N buses, the centre position is (N + 1) / 2 from the left. Step 5: Equate these: N - 41 = (N + 1) / 2. Step 6: Multiply by 2: 2N - 82 = N + 1, which gives N = 83. Step 7: The central position from the left is (83 + 1) / 2 = 42, so Raftaar's position from the left is 42. Step 8: The leftmost bus is at position 1. Buses strictly between position 1 and position 42 are from position 2 to position 41. Step 9: Count of buses between them = 41 - 2 + 1 = 40.
Verification / Alternative check:
We can quickly confirm the values: Panjab from left = N - 18 = 83 - 18 = 65. Distance between Raftaar (42) and Panjab (65) is 23 places, which matches the question. This confirms that our interpretation and calculations are consistent.

Why Other Options Are Wrong:
44, 42, 46, 38: All these alternatives correspond to different assumed totals of buses or incorrect counting of buses between two positions. They arise if someone mistakenly includes one of the endpoints or miscomputes the central position.
Common Pitfalls:
A frequent mistake is to misinterpret “between” and accidentally include one or both endpoint positions in the count. Another error is forgetting to adjust the formula N - rank from right + 1 when converting to rank from the left. Finally, some test takers incorrectly assume an even number of buses, which would not allow a single exact middle bus as described in the problem.

Final Answer:
The number of buses between Raftaar and the bus at the left end is 40.