Match each set of elevation and ground distance measurements to its corresponding slope gr… — JAMB UTME

Match each set of elevation and ground distance measurements to its corresponding slope gradient ratio.

Vertical Interval of $50\text{ m}$ across a Horizontal Equivalent of $1\text{ km}$ $1 \text{ in } 20$
Vertical Interval of $100\text{ m}$ across a Horizontal Equivalent of $500\text{ m}$ $1 \text{ in } 5$
Vertical Interval of $200\text{ m}$ across a Horizontal Equivalent of $2\text{ km}$ $1 \text{ in } 10$
Vertical Interval of $40\text{ m}$ across a Horizontal Equivalent of $2\text{ km}$ $1 \text{ in } 50$

The measurements correctly match their gradient ratios as follows:

50\text{ m} / 1,000\text{ m}

matches

1 \text{ in } 20

;

100\text{ m} / 500\text{ m}

matches

1 \text{ in } 5

;

200\text{ m} / 2,000\text{ m}

matches

1 \text{ in } 10

; and

40\text{ m} / 2,000\text{ m}

matches

1 \text{ in } 50

Each pair is matched by ensuring both the Vertical Interval and Horizontal Equivalent are in meters, applying

\text{Gradient} = \frac{\text{V.I.}}{\text{H.E.}}

, and reducing the fraction to

1 \text{ in } N

form.

Convert all Horizontal Equivalent values into meters so that units match the Vertical Interval.

1\text{ km} = 1,000\text{ m}

and

2\text{ km} = 2,000\text{ m}

Gradient calculation requires both vertical and horizontal measurements to be in identical linear units.

Apply the slope gradient formula:

\text{Gradient} = \frac{\text{Vertical Interval (V.I.)}}{\text{Horizontal Equivalent (H.E.)}}

Form fractions for each pair:

\frac{50}{1000}

\frac{100}{500}

\frac{200}{2000}

, and

\frac{40}{2000}

Establishes the ratio between vertical rise and horizontal distance.

Simplify each fraction to unit numerator format (

1 \text{ in } N

Ratios simplify to

1 \text{ in } 20

1 \text{ in } 5

1 \text{ in } 10

, and

1 \text{ in } 50

Standard expression of slope gradient in geography mapwork.

Calculating slope gradient using Vertical Interval (V.I.) divided by Horizontal Equivalent (H.E.) in uniform units.

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