On a topographical map drawn to a scale of 1 : 50,000, Point X is situated at an elevation… — JAMB UTME

On a topographical map drawn to a scale of $1 : 50,000$ , Point X is situated at an elevation of $150\text{ m}$ and Point Y is situated at an elevation of $400\text{ m}$ . If the straight-line distance between Point X and Point Y measured on the map is $5\text{ cm}$ , what is the slope gradient between the two points expressed as a percentage?

A
$0.1\%$
$10\%$ Answer
C
$16\%$
D
$5\%$

Answer

The slope gradient between Point X and Point Y expressed as a percentage is

10\%

To find the gradient percentage, first calculate the Vertical Interval (VI):

400\text{ m} - 150\text{ m} = 250\text{ m}

. Next, calculate the Horizontal Equivalent (HE):

5\text{ cm} \times 50,000 = 250,000\text{ cm} = 2,500\text{ m}

. Expressing VI over HE gives

\frac{250\text{ m}}{2,500\text{ m}} = \frac{1}{10}

. Converting this fraction to a percentage gives

1/10 \times 100\% = 10\%

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 400\text{ m} - 150\text{ m} = 250\text{ m}

The Vertical Interval is the difference in elevation between the higher point and lower point.

Calculate the Horizontal Equivalent (HE) in meters

\text{HE} = 5\text{ cm} \times 50,000 = 250,000\text{ cm} = 2,500\text{ m}

Multiply the map distance by the scale denominator to find ground distance, then convert centimeters to meters.

Compute the slope gradient as a fraction and convert to percentage

\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{250\text{ m}}{2,500\text{ m}} = 0.10 = 10\%

Gradient percentage is calculated by dividing Vertical Interval by Horizontal Equivalent in identical units and multiplying by

100\%

Key Concept

Slope and Gradient Calculation

Estimated Time:2m 0s

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