On a topographical map with a scale of 1 : 50,000, Point X lies on a hilltop at an elevati… — JAMB UTME

On a topographical map with a scale of $1 : 50,000$ , Point X lies on a hilltop at an elevation of $420\text{ m}$ , while Point Y sits near a stream bed at an elevation of $170\text{ m}$ . If the measured distance between Point X and Point Y on the map is $12.5\text{ cm}$ , calculate the slope gradient between the two points. Express your answer as the value of $N$ in the standard gradient ratio $1 : N$ (or $1 \text{ in } N$ ). What is the value of $N$ ?

Answer: 25 ratio denominator

Answer

The denominator N in the gradient ratio 1 : N is 25.

The vertical interval (V.I.) between the hilltop at

420\text{ m}

and the stream at

170\text{ m}

250\text{ m}

. The horizontal equivalent (H.E.) on the ground is calculated by multiplying the map distance of

12.5\text{ cm}

by the map scale factor of

50,000

, which gives

625,000\text{ cm}

(

6,250\text{ m}

). Dividing V.I. by H.E. yields

250 / 6,250 = 1 / 25

. Thus, the gradient ratio is

1 : 25

, making

N = 25

Step-by-Step Solution

Calculate Vertical Interval (V.I.)

V.I. = 420 m - 170 m = 250 m

Vertical interval is the difference in height between the highest and lowest points.

Convert map distance to ground distance to determine Horizontal Equivalent (H.E.) in meters

H.E. = 12.5 cm × 50,000 = 625,000 cm = 6,250 m

Horizontal equivalent must be in the same units as the vertical interval before computing ratio.

Divide V.I. by H.E. to express the gradient as a ratio 1 : N

Gradient = 250 / 6,250 = 1 / 25

Simplifying the fraction V.I. / H.E. yields 1 / 25, giving N = 25.

Key Concept

Slope and Gradient Calculation

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