Map Enlargement and Reduction

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?

A map drawn at a scale of $1 : 50,000$ is enlarged to twice its original linear dimensions. Calculate the denominator of the new Representative Fraction (R.F.) scale.

A topographical map with a scale of $1 : 100,000$ depicts a reservoir that covers an area of $16\text{ cm}^2$ on the map. If the map is reduced to a new scale of $1 : 250,000$, what is the area of the reservoir on the new reduced map in square centimeters ($\text{cm}^2$)?

A farm settlement measures $6\text{ cm}$ by $8\text{ cm}$ on a topographical map drawn at a scale of $1 : 40,000$. If the map is enlarged to a new scale of $1 : 10,000$, what is the area of the farm settlement on the enlarged map?

A wildlife sanctuary occupies an area of $48\text{ cm}^2$ on a topographical map drawn at a scale of $1 : 100,000$. If the map is reduced to a new scale of $1 : 400,000$, what is the area of the sanctuary on the new map in $\text{cm}^2$?

A straight segment of a proposed highway measures $10\text{ cm}$ on a topographic map drawn at a scale of $1 : 50,000$. On a newly redrawn map, the same segment of highway measures $25\text{ cm}$. What is the Representative Fraction (R.F.) scale of the new map?

A forest reserve covers an area of $16\text{ cm}^2$ on a topographical map with a scale of $1 : 100,000$. If the map is enlarged such that the same forest reserve occupies an area of $64\text{ cm}^2$ on the new map, what is the scale denominator ($N$) of the new map, where the scale is expressed as $1 : N$?

A coastal lagoon covers a rectangular section measuring $12\text{ cm}$ by $15\text{ cm}$ on Map A, which is drawn to a scale of $1 : 20,000$. If Map A is reduced to create Map B with a scale of $1 : 60,000$, what is the area of the lagoon on Map B in square centimeters?

A rectangular agricultural estate measuring $5\text{ cm}$ by $12\text{ cm}$ on a topographical map represents an actual ground area of $60\text{ km}^2$. If the map is enlarged such that the estate covers an area of $240\text{ cm}^2$ on the new map, what is the denominator of the Representative Fraction (RF) scale of the enlarged map?

A river basin covers a rectangular section measuring $4.5\text{ cm}$ by $8\text{ cm}$ on Map X, which has a representative fraction of $1 : 25,000$. Map X is enlarged to create Map Y, where the same river basin occupies an area of $144\text{ cm}^2$. Map Y is then reduced to construct Map Z, such that the denominator of Map Z's representative fraction is $4$ times that of Map Y. What is the area of the river basin on Map Z in $\text{cm}^2$?

A topographical map drawn to a Representative Fraction (R.F.) scale of $1 : 50,000$ is enlarged to twice its original linear dimensions. What is the scale of the new enlarged map?

A county boundary encloses an area of $72\text{ cm}^2$ on Map A, which is drawn at a scale of $1 : 20,000$. Map A is reduced to produce Map B, which has a Representative Fraction of $1 : 60,000$. What is the area of the county boundary on Map B?

A wildlife sanctuary covers an area of $36\text{ cm}^2$ on Map X, which is drawn to a scale of $1 : 40,000$. If the map is reduced to a scale of $1 : 120,000$, what is the area of the sanctuary on the new map?

A forest reserve covers an area of $18\text{ cm}^2$ on a topographical map drawn to a scale of $1 : 150,000$. If the map is enlarged so that a statement scale of $1\text{ cm}$ to $0.5\text{ km}$ is used for the new map, what is the area of the forest reserve on the enlarged map in $\text{cm}^2$?

On Map X, drawn at a scale of $1 : 25,000$, a planned agricultural settlement occupies a square grid block measuring $4\text{ cm}$ by $4\text{ cm}$. Map X is reduced to produce Map Y such that the same agricultural settlement occupies a reduced area of $1\text{ cm}^2$. What is the Representative Fraction (R.F.) scale of Map Y?

A topographical map, Map A, drawn to a scale of $1 : 100,000$, displays a rectangular reservoir measuring $5\text{ cm}$ by $8\text{ cm}$. When Map A is reduced to create Map B, the reservoir covers an area of $10\text{ cm}^2$ on Map B. What is the representative fraction (R.F.) scale of Map B?

A mining concession covers an area of $40\text{ cm}^2$ on a topographical map drawn to a scale of $1 : 50,000$. If this map is reduced to a scale of $1 : 200,000$, what is the area of the concession on the reduced map in $\text{cm}^2$?

A wildlife sanctuary covers an area of $24\text{ cm}^2$ on Map P, which is drawn to a scale of $1 : 60,000$. If Map P is enlarged to produce Map Q with a scale of $1 : 20,000$, what is the area of the sanctuary on Map Q in $\text{cm}^2$?

A proposed industrial estate is represented as a square measuring $6\text{ cm}$ by $6\text{ cm}$ on a topographical map drawn to a scale of $1 : 40,000$. If the map is reduced to a scale of $1 : 120,000$, what is the new area of the industrial estate on the reduced map?

A forest reserve is represented as a rectangular feature measuring $8\text{ cm}$ by $10\text{ cm}$ on Map X, which is drawn to a scale of $1 : 50,000$. On a newly drawn map, Map Y, the same forest reserve occupies an area of $320\text{ cm}^2$. What is the representative fraction scale of Map Y?