Question

A map of 10 cm x 8 cm represents an area of 50000 square meter of a field. The r.F. Of the scale is

Answer 1

The RF of the scale is 1:62500000

Representing Fraction(RF) is defined as the ratio of size of the drawing and the size of the object.

Area in the map = 10 x 8 = 80 cm² = 8 x 10⁻³ m²

Actual Area of the field = 50000 m² = 5 x 10⁴ m²

Hence,

RF = 8 x 10⁻³/5 x 10⁴ = 1.6/10⁸ = 1/0.625x10⁸ = 1: 62500000

Hence the Representing fraction(RF) of the map is 1:62500000

clearly we can see that the RF  < 1 , hence it is a Reducing scale.

Answer 2

Area of the Map = 10 × 8 cm² = 80 cm².

Area of the Field = 50,000 m²

Now, R.F. or Representative Fraction scale (or K) = Area of the Map/Area of the Field.

= 80/50,000

= 1/625

This means that 625 m² area on the Field is equivalent to the 1 cm² on the map.

It may be possible that some peoples may define that by using the Reverse condition, Means by taking R.F. as Area on Filed/Area of Map, but both will have the same meaning.

Hope it helps.