A topographical map displays a statement scale of 2\text{ cm} to 1\text{ km}. Which of the… — JAMB UTME

A topographical map displays a statement scale of $2\text{ cm}$ to $1\text{ km}$ . Which of the following represents this scale as a Representative Fraction (R.F.)?

A
$50,000 : 1$
$1 : 50,000$ Answer
C
$1 : 2,500,000$
D
$1 : 500$

Answer

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

1 : 50,000

The correct Representative Fraction is

1 : 50,000

. Converting

1\text{ km}

into centimeters yields

100,000\text{ cm}

. Expressing the scale as a ratio gives

2\text{ cm} : 100,000\text{ cm}

, which simplifies to

1 : 50,000

when both terms are divided by

2

Step-by-Step Solution

Convert the ground distance from kilometers to centimeters so both sides of the scale ratio share identical units.

1\text{ km} = 100,000\text{ cm}

Representative Fraction requires unitless comparison, so both map distance and ground distance must be in the same measurement units.

Express the relationship as a ratio of map distance to ground distance.

\text{Scale} = 2\text{ cm} : 100,000\text{ cm}

A Representative Fraction is written in the form

1 : n

, where

1

represents map distance and

n

represents ground distance.

Divide both terms of the ratio by the map distance value (

2

) to reduce the numerator/antecedent to

1

\frac{2}{2} : \frac{100,000}{2} = 1 : 50,000

Simplifying the antecedent to unity gives the final standard Representative Fraction format.

Key Concept

Conversion of Statement Scale to Representative Fraction (R.F.)

Estimated Time:45s

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Step-by-Step Solution

Key Concept

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