Question

Population of Rajasthan is 570 lakhs and the population of UP is 1660 lakhs. Area of Rajasthan is $3\ lakh\ k{{m}^{2}}$ and the area of UP is $2\ lakh\ k{{m}^{2}}$.
(i) How many people are there $\ per\ k{{m}^{2}}$ in both these states?
(ii) Which state is less densely populated?

Answer 1

Hint: When you see the problems or questions like this then first the unitary method should come in your mind, sometimes it works direct for your problem and sometime reverse unitary method will works in solving problem like find the value of multiple things by multiplying value of same one thing then we need to divide by that value which for we need a value.

Complete step by step answer:
(i) Here, we need to find the number of people $\ per\ k{{m}^{2}}$in both Rajasthan and UP state; it means we need to find the value as a number of people for a $k{{m}^{2}}$area.
$\begin{align}
  & People\ per\ k{{m}^{2}}\ in\ Rajasthan\ =\dfrac{Population\ of\ Rajasthan}{Area\ of\ Rajasthan} \\
 & People\ per\ k{{m}^{2}}\ in\ Rajasthan\ =\dfrac{570\times {{10}^{5}}}{3\times {{10}^{5}}k{{m}^{2}}}=190\ people\ per\ k{{m}^{2}} \\
\end{align}$
Same for UP,
$\begin{align}
  & People\ per\ k{{m}^{2}}\ in\ UP\ =\dfrac{Population\ of\ UP}{Area\ of\ UP} \\
 & People\ per\ k{{m}^{2}}\ in\ UP\ =\dfrac{1660\times {{10}^{5}}}{2\times {{10}^{5}}k{{m}^{2}}}=830\ people\ per\ k{{m}^{2}} \\
\end{align}$
Hence, $190\ people\ per\ k{{m}^{2}}$are in Rajasthan and $830\ people\ per\ k{{m}^{2}}$are in UP.
(ii) Rajasthan is less densely populated state from Rajasthan and UP, because we see in part (i) only 190 peoples are in $1k{{m}^{2}}$area, where UP have 830 peoples in $1k{{m}^{2}}$area.

Note: Do not estimate the answer of simple problems, sometimes data gives the value very near which can confuse us and lose marks in simple problems.Here the total population of Rajasthan at times might be greater than other given states but per sq km is a different quantity and need not always be greater than the other or vice versa.