In a straight row of 65 parked vehicles, a red sedan is 24th from the left end, and a blue SUV is 18th from the right end. How many vehicles are parked between the red sedan and the blue SUV?

The correct answer is 23.

Step-by-Step Explanation:

To find the number of vehicles parked between the red sedan and the blue SUV, we can either use the formula for non-overlapping ranks or convert both positions relative to the same end of the row.

Given Data:
Total number of parked vehicles = 65
Position of the red sedan from the left end = 24^th
Position of the blue SUV from the right end = 18^th

Method 1: Direct Non-Overlapping Calculation

First, calculate the sum of the positions of both vehicles from their respective ends:

$\text{Sum of positions}=24+18=42$

Since the sum of their positions (42) is strictly less than the total number of vehicles (65), the two vehicles do not overlap in position.

The formula for the number of vehicles between two objects in a non-overlapping row is:

$\text{Vehicles between}=\text{Total vehicles}-(\text{Position from left}+\text{Position from right})$

Substitute the given values into the equation:

$\text{Vehicles between}=65-(24+18)$

$\text{Vehicles between}=65-42=23$

Method 2: Converting Positions to the Same End

We can also determine the position of the blue SUV from the left end using the standard ranking formula:

$\text{Position of SUV from left}=\text{Total vehicles}-\text{Position from right}+1$

$\text{Position of SUV from left}=65-18+1=48$

Now, calculate the number of vehicles lying between the 24^th position and the 48^th position:

$\text{Vehicles between}=48-24-1=23$

Therefore, there are 23 vehicles parked between the red sedan and the blue SUV.