On a topographical map, Point X is situated at an elevation of 200\text{ m} and Point Y is… — JAMB UTME

On a topographical map, Point X is situated at an elevation of $200\text{ m}$ and Point Y is situated at an elevation of $500\text{ m}$ . If the horizontal ground distance between the two points is $6\text{ km}$ , what is the gradient of the slope from Point X to Point Y expressed as a ratio?

$1 : 20$ Answer
B
$1 : 2$
C
$1 : 12$
D
$20 : 1$

Answer

The gradient of the slope between Point X and Point Y is

1 : 20

The correct ratio

1 : 20

is obtained by subtracting the lower elevation (

200\text{ m}

) from the higher elevation (

500\text{ m}

) to obtain a vertical interval of

300\text{ m}

, converting the horizontal distance of

6\text{ km}

into

6,000\text{ m}

, and simplifying the fraction

\frac{300}{6000}

\frac{1}{20}

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 500\text{ m} - 200\text{ m} = 300\text{ m}

Vertical interval is the difference in elevation between the higher and lower points.

Convert the Horizontal Equivalent (HE) to the same units as VI

\text{HE} = 6\text{ km} \times 1,000 = 6,000\text{ m}

Both vertical difference and horizontal distance must be expressed in identical units (meters).

Compute the slope gradient as a ratio

\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{300\text{ m}}{6,000\text{ m}} = \frac{1}{20} = 1 : 20

Gradient is calculated by dividing Vertical Interval by Horizontal Equivalent and simplifying to a ratio of 1 in N.

Key Concept

Calculating topographic gradient using Vertical Interval (VI) and Horizontal Equivalent (HE)

Estimated Time:45s

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