Four survey transects were evaluated on a topographical map drawn to a scale of 1 : 50,000… — JAMB UTME

Four survey transects were evaluated on a topographical map drawn to a scale of $1 : 50,000$ . Match each transect scenario on the left with its corresponding calculated slope gradient ratio on the right.

Transect P: Vertical interval of $100\text{ m}$ across a map distance of $5\text{ cm}$ $1 \text{ in } 25$
Transect Q: Vertical interval of $250\text{ m}$ across a map distance of $2\text{ cm}$ $1 \text{ in } 4$
Transect R: Vertical interval of $60\text{ m}$ across a map distance of $6\text{ cm}$ $1 \text{ in } 50$
Transect S: Vertical interval of $150\text{ m}$ across a map distance of $3\text{ cm}$ $1 \text{ in } 10$

Answer

Transect P matches

1 \text{ in } 25

; Transect Q matches

1 \text{ in } 4

; Transect R matches

1 \text{ in } 50

; Transect S matches

1 \text{ in } 10

Each scenario is correctly matched by converting map distance to real-world ground distance (HE) using the

1 : 50,000

scale multiplier (

1\text{ cm} = 500\text{ m}

) and then computing rise over run (VI / HE).

Step-by-Step Solution

Convert map distances to Horizontal Equivalent (HE) in meters for each transect using the map scale ratio (

1 : 50,000

, where

1\text{ cm} = 500\text{ m}

Transect P HE:

5\text{ cm} \times 500\text{ m/cm} = 2,500\text{ m}

; Transect Q HE:

2\text{ cm} \times 500\text{ m/cm} = 1,000\text{ m}

; Transect R HE:

6\text{ cm} \times 500\text{ m/cm} = 3,000\text{ m}

; Transect S HE:

3\text{ cm} \times 500\text{ m/cm} = 1,500\text{ m}

Gradient calculation requires both Vertical Interval (VI) and Horizontal Equivalent (HE) to be in identical linear measurement units.

Calculate the slope gradient for each transect using the formula

\text{Gradient} = \frac{\text{VI}}{\text{HE}}

and simplify to ratio form (

1 \text{ in } N

Transect P:

\frac{100\text{ m}}{2,500\text{ m}} = \frac{1}{25} = 1 \text{ in } 25

; Transect Q:

\frac{250\text{ m}}{1,000\text{ m}} = \frac{1}{4} = 1 \text{ in } 4

; Transect R:

\frac{60\text{ m}}{3,000\text{ m}} = \frac{1}{50} = 1 \text{ in } 50

; Transect S:

\frac{150\text{ m}}{1,500\text{ m}} = \frac{1}{10} = 1 \text{ in } 10

Expressing

\frac{\text{VI}}{\text{HE}}

as a unit fraction yields the standard ratio representation used in topographic map reading.

Key Concept

Slope gradient is the ratio of vertical elevation change (Vertical Interval) to ground horizontal distance (Horizontal Equivalent), expressed as a fraction or ratio

1 \text{ in } N

Question

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Key Concept

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