A topographical map drawn at a scale of 1 : 20,000 is reduced to one-fourth of its origina… — JAMB UTME

A topographical map drawn at a scale of $1 : 20,000$ is reduced to one-fourth of its original linear size. What is the Representative Fraction (R.F.) of the new map?

$1 : 80,000$ Answer
B
$1 : 5,000$
C
$1 : 320,000$
D
$1 : 40,000$

Answer

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

1 : 80,000

When a map is reduced to one-fourth of its linear size, ground distances are represented by one-fourth as much length on the new map. Therefore, the scale denominator must be multiplied by

4

20,000 \times 4 = 80,000

, yielding a new Representative Fraction of

1 : 80,000

Step-by-Step Solution

Identify the original scale denominator and the linear reduction factor

Original denominator =

20,000

; Linear reduction factor =

4

times smaller linear dimensions

When a map is reduced linearly by a factor of

n

, its new scale denominator becomes

n

times larger.

Calculate the new scale denominator

New scale denominator =

20,000 \times 4 = 80,000

A smaller scale map covers ground features in less space, which requires a larger denominator in the ratio scale.

Key Concept

Linear Map Reduction Scale Calculation

Question

Answer

Step-by-Step Solution

Key Concept

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