Question

Population of Rajasthan $=570\mathrm{lakhs}$ and population of UP $=1660\mathrm{lakhs}$. Area of Rajasthan $=3\mathrm{lakh}{\mathrm{km}}^2$ and area of UP $=2\mathrm{lakh}{\mathrm{km}}^2$.

(i) How many people are there per ${\mathrm{km}}^2$ in both these States?

(ii) Which State is less populated?

Answer 1

Step 1. Determine the number of people per ${\mathrm{km}}^2$ in Rajasthan.

It is given that Rajasthan has a population $=570\mathrm{lakhs}$, the population of Uttar Pradesh $=1660\mathrm{lakhs}$, Rajasthan has a total area $=3\mathrm{lakh}{\mathrm{km}}^2$, and UP has a total area $=2\mathrm{lakh}{\mathrm{km}}^2$.

Rajasthan has a population $=570\mathrm{lakhs}$

Rajasthan has a total area $=3\mathrm{lakh}{\mathrm{km}}^2$

The population of Rajasthan per ${\mathrm{km}}^2$ is as follows:

$\begin{array}{rcl}\mathrm{Population}\mathrm{per}{\mathrm{km}}^2& =& \frac{570\mathrm{lakh}}{3\mathrm{lakh}}\\ & \Rightarrow & \mathrm{Population}\mathrm{per}{\mathrm{km}}^2=190\end{array}$

Therefore, the population of Rajasthan is $190$ persons per square kilometer.

Step 2: Determine the number of people per ${\mathrm{km}}^2$ in UP.

UP has a population $=1660\mathrm{lakhs}$

UP has a total area $=2\mathrm{lakh}{\mathrm{km}}^2$

The population of UP per ${\mathrm{km}}^2$ is as follows:

$\begin{array}{rcl}\mathrm{Population}\mathrm{per}{\mathrm{km}}^2& =& \frac{1660\mathrm{lakh}}{2\mathrm{lakh}}\\ & \Rightarrow & \mathrm{Population}\mathrm{per}{\mathrm{km}}^2=830\end{array}$

Therefore, the population of UP is $830$ persons per square kilometer.

Step 3: Determine which state has less population.

UP has a population of $830$ persons per square kilometer and Rajasthan has a population of $190$ persons per square kilometer.

So, by comparing the population in the two given states, we can see that Rajasthan has less population than UP.

Hence, Rajasthan is a less populated state.