Match each slope measurement scenario on the left with its corresponding calculated gradie… — JAMB UTME

Match each slope measurement scenario on the left with its corresponding calculated gradient on the right.

Vertical Interval $= 80\text{ m}$ , Horizontal Equivalent $= 1.6\text{ km}$ $1 \text{ in } 20$ (or $5\%$ )
Vertical Interval $= 150\text{ m}$ , Horizontal Equivalent $= 600\text{ m}$ $1 \text{ in } 4$ (or $25\%$ )
Vertical Interval $= 50\text{ m}$ , Horizontal Equivalent $= 2.5\text{ km}$ $1 \text{ in } 50$ (or $2\%$ )
Vertical Interval $= 200\text{ m}$ , Horizontal Equivalent $= 1\text{ km}$ $1 \text{ in } 5$ (or $20\%$ )

Answer

Vertical Interval = 80 m, HE = 1.6 km matches 1 in 20 (5%); VI = 150 m, HE = 600 m matches 1 in 4 (25%); VI = 50 m, HE = 2.5 km matches 1 in 50 (2%); VI = 200 m, HE = 1 km matches 1 in 5 (20%).

Each scenario is correctly matched by converting all horizontal distances into meters and calculating the simplified ratio VI / HE, expressed as both a ratio (1 in N) and a percentage.

Step-by-Step Solution

Convert all Horizontal Equivalent (HE) distances given in kilometers to meters so that units match the Vertical Interval (VI).

1.6\text{ km} = 1,600\text{ m}

2.5\text{ km} = 2,500\text{ m}

, and

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

Both Vertical Interval and Horizontal Equivalent must be in the same units of measurement before calculating the ratio.

Apply the gradient formula

\text{Gradient} = \frac{\text{Vertical Interval (VI)}}{\text{Horizontal Equivalent (HE)}}

to each scenario.

Scenario 1:

\frac{80}{1600} = \frac{1}{20}

; Scenario 2:

\frac{150}{600} = \frac{1}{4}

; Scenario 3:

\frac{50}{2500} = \frac{1}{50}

; Scenario 4:

\frac{200}{1000} = \frac{1}{5}

Dividing vertical rise by horizontal distance yields the simplified slope fraction.

Express each simplified fraction in standard ratio (

1 \text{ in } N

) and percentage formats.

\frac{1}{20} = 1\text{ in } 20\ (5\%)

\frac{1}{4} = 1\text{ in } 4\ (25\%)

\frac{1}{50} = 1\text{ in } 50\ (2\%)

\frac{1}{5} = 1\text{ in } 5\ (20\%)

This allows matching the calculated values directly to the corresponding choices on the right.

Key Concept

Slope and gradient calculation using Vertical Interval (VI) and Horizontal Equivalent (HE) with unit unification.

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