A topographic map with an original scale of 1 : 50,000 is reduced to half its linear size.… — JAMB UTME

A topographic map with an original scale of $1 : 50,000$ is reduced to half its linear size. On the reduced map, the measured distance between Point X (elevation $750\text{ m}$ ) and Point Y along a slope is $5.0\text{ cm}$ . If Point Y lies $8$ contour intervals below Point X on a map with a contour interval of $25\text{ m}$ , what is the gradient between Point X and Point Y expressed as a ratio?

A
$1 \text{ in } 6.25$
$1 \text{ in } 25$ Answer
C
$1 \text{ in } 40$
D
$1 \text{ in } 20$

Answer

The gradient between Point X and Point Y is

1 \text{ in } 25

The gradient expressed as

1 \text{ in } 25

is correct because reducing a

1 : 50,000

map to half its linear size yields a scale of

1 : 100,000

. At this scale,

5.0\text{ cm}

corresponds to a Horizontal Equivalent (HE) of

5,000\text{ m}

. With

8

contour intervals at

25\text{ m}

each, the Vertical Interval (VI) is

200\text{ m}

. Dividing VI by HE gives

\frac{200}{5,000} = \frac{1}{25}

Step-by-Step Solution

Determine the new map scale after linear reduction

New Scale =

1 : 100,000

Reducing a map to half its linear size doubles the scale denominator (

50,000 \times 2 = 100,000

Calculate the Horizontal Equivalent (HE) ground distance

\text{HE} = 5.0\text{ cm} \times 100,000 = 500,000\text{ cm} = 5,000\text{ m}

Multiply map distance by the new scale factor and convert centimeters to meters.

Calculate the Vertical Interval (VI) between Point X and Point Y

\text{VI} = 8 \times 25\text{ m} = 200\text{ m}

Multiply the number of contour intervals by the contour interval value.

Compute the gradient ratio

\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{200\text{ m}}{5,000\text{ m}} = \frac{1}{25}

1 \text{ in } 25

Divide Vertical Interval by Horizontal Equivalent in identical units to find the simple ratio.

Key Concept

Topographic Gradient and Map Scale Reduction

Estimated Time:3m 0s

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