On a straight railway track, a sequence of freight carriages is standing in a single line.… — State PSC Exam

On a straight railway track, a sequence of freight carriages is standing in a single line. Carriage $X$ is the $38^{\text{th}}$ carriage from the front end, and Carriage $Y$ is the $47^{\text{th}}$ carriage from the rear end. Carriage $Z$ is positioned exactly halfway between Carriage $X$ and Carriage $Y$ . If Carriage $Z$ is the $62^{\text{nd}}$ carriage from the rear end, what is the total number of freight carriages on the track?

Answer: 114

Answer

114

The positional distance between Carriage

Y

and Carriage

Z

from the rear is 15. Since

Z

is the midpoint, Carriage

X

is another 15 positions ahead, making

X

the

77^{\text{th}}

carriage from the rear. Since

X

is also

38^{\text{th}}

from the front, the total number of carriages is calculated as

38 + 77 - 1 = 114

Step-by-Step Solution

Calculate the positional difference between Carriage

Y

and Carriage

Z

from the rear.

62 - 47 = 15

positions.

To find the distance from one end of the segment to its exact midpoint.

Determine Carriage

X

's position from the rear.

Carriage

X

is the

77^{\text{th}}

carriage from the rear.

Since

Z

is exactly halfway between

X

and

Y

, the positional difference between

Z

and

X

must also be 15. Thus,

62 + 15 = 77

Calculate the total number of carriages.

38 + 77 - 1 = 114

carriages.

The total number of items in a row equals (Position from front) + (Position from rear) - 1.

Key Concept

Calculating total count using dual positional ranks and midpoint symmetry in a sequence.

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