In a linear arrangement of food stalls at a weekend night market, the "Spice Hub" stall is… — State PSC Exam

In a linear arrangement of food stalls at a weekend night market, the "Spice Hub" stall is positioned $18^{\text{th}}$ from the left end, and the "Grill Master" stall is positioned $25^{\text{th}}$ from the right end. If the two stalls interchange their exact positions, the "Spice Hub" stall becomes $31^{\text{st}}$ from the left end. Based on this new arrangement, what is the total number of food stalls in the row?

A
$56$
$55$ Answer
C
$48$
D
$42$

Answer

The total number of food stalls is

55

By interchanging positions, "Spice Hub" moves to the spot originally held by "Grill Master". We know this specific spot is

25^{\text{th}}

from the right end. The problem states that "Spice Hub" is now

31^{\text{st}}

from the left end. Since we have both the left rank (

31

) and the right rank (

25

) for the exact same physical position, we can find the total by adding them and subtracting

1

to correct for double-counting the stall itself:

31 + 25 - 1 = 55

Step-by-Step Solution

Identify a single physical position where both the left and right ranks are known.

After the interchange, the new position of "Spice Hub" is the original position of "Grill Master".

To calculate the total number of items in a row, we need the exact distance from both ends for the exact same point.

Determine the specific left and right ranks for this identified position.

The position is

25^{\text{th}}

from the right (original "Grill Master" rank) and

31^{\text{st}}

from the left (new "Spice Hub" rank).

The physical location of the stall hasn't changed relative to the ends, only the stall occupying it has changed.

Apply the total rank formula:

\text{Total} = \text{Left Rank} + \text{Right Rank} - 1

\text{Total} = 31 + 25 - 1 = 55

We must subtract

1

because adding the left and right ranks counts the stall at that specific position twice.

Key Concept

Positional Ranking and Interchange

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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