Two agricultural processing centers in Osun State are separated by an actual ground distan… — JAMB UTME

Two agricultural processing centers in Osun State are separated by an actual ground distance of $7.5\text{ km}$ . If the distance between these two centers on a regional planning map measures $15\text{ cm}$ , what is the Representative Fraction (R.F.) of the map?

$1 : 50,000$ Answer
B
$50,000 : 1$
C
$1 : 5,000$
D
$1 : 500,000$

Answer

The Representative Fraction (R.F.) of the map is

1 : 50,000

To find the Representative Fraction, first convert

7.5\text{ km}

to centimeters (

7.5 \times 100,000 = 750,000\text{ cm}

). Setting up the ratio of map distance to ground distance gives

\frac{15}{750,000}

, which reduces to

\frac{1}{50,000}

, yielding an R.F. of

1 : 50,000

Step-by-Step Solution

Convert the ground distance from kilometers to centimeters.

7.5\text{ km} \times 100,000\text{ cm/km} = 750,000\text{ cm}

Representative Fraction requires both map distance and ground distance to be in identical units.

Formulate the ratio of map distance to ground distance.

\text{Scale} = \frac{15\text{ cm}}{750,000\text{ cm}}

The formula for Representative Fraction is

\text{R.F.} = \frac{\text{Map Distance}}{\text{Ground Distance}}

Simplify the fraction to have a numerator of 1.

\frac{15 \div 15}{750,000 \div 15} = \frac{1}{50,000}

1 : 50,000

An R.F. must always be expressed as a unit fraction (

1 : n

Key Concept

Calculating Representative Fraction (R.F.) from map distance and ground distance

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