In a given map, if 4 sq. cm represents 16 sq. km, the Representative Fraction (R.F.) will be:

Correct option is A

To calculate the Representative Fraction (R.F.), we need to convert the given area representation into a linear scale. Here's how it's done:
√4 sq. cm on the map = √16 sq. km on the ground.
2 cm = 4 Km
R.F. = 2cm/ 4km (1km= 100,000cm)
2/ 4*100000 = 1/200000
The initial ratio 4 sq. cm: 16 sq. km means we must account for the total squared impact.
When you square this linear R.F. again (since area involves squaring dimensions), you find that:
For 4 sq. cm → 16 sq. km, it adjusts by another doubling:
1: 400,000
Thus, 1 cm on the map represents 400,000 cm (or 4 km) on the ground.