Question

As per the 2011 census, the population of India and a few of its states is given below:

Total population of India = 12,101 lakh

Total area of India (excluding the area of J&K under illegal occupation of Pakistan and China)

= 31.7 lakh.sq km.

Total cultivated area of India = 14.28 lakh sq km.

S. No.	Name of the state	Population (in lakhs)	Area (lakh sq. km.)
1.	Arunachal Pradesh	13.8	8.36
2.	Bihar	1038.0	17.39
3.	Kerala	333.9	3.89
4.	Uttar Pradesh	1995.8	2.94
5.	West Bengal	913.5	8.78

Study the above data and answer the questions that follow:

1. Find out the Arithmetic density and Physiological density for India.
2. Which state has the lowest density?
3. Which state has the highest density?

Answer 1

i. Total population of India = 12,101 lakh     ...Given

Total area of India = 31.7 lakh sq km       ...Given

Total cultivated area = 14.28 lakh sq km     ...Given

Arithmetic Density = `"Total population"/"Total area"`

= `12101/31.7`

= 381.6 persons per sq km

Physiological Density = `"Total population"/"Cultivated area"`

= `12101/14.28`

= 847.5 persons per sq km

ii. Density = `"Population"/"Area"`

1. Arunachal Pradesh = `13.8/8.36 = 1.65` persons per sq km 
2. Bihar = `1038.0/17.39 = 59.7` persons per sq km
3. Kerala = `333.9/3.89 = 85.8` persons per sq km
4. Uttar Pradesh = `1995.8/2.94 = 679.0` persons per sq km
5. West Bengal = `913.5/8.78 = 104.1` persons per sq km

Therefore, Arunachal Pradesh has the lowest density.

iii. Uttar Pradesh: 679.0 persons/sq km

Therefore, Uttar Pradesh has the highest density among the listed states.