Question

If in the year 1998, there was an increase of 10% in the population of U.P. and 12% in the population of M.P. compared to the previous year, then what was the ratio of populations of U.P. and M.P. in 1997?

$\left( {\text{A}} \right){\text{ }}42:55$
$\left( {\text{B}} \right){\text{ }}48:55$
$\left( {\text{C}} \right){\text{ }}7:11$
$\left( {\text{D}} \right){\text{ }}4:5$

Answer 1

Hint: To find out the ratio of U.P. and M.P. in $1997$. Here, the population for the states in $1998$ is given in percentage and the total population is also given. We need to calculate the population in absolute terms using the percentages.

Formula used:
Here, we will use the formula of percentage to find the absolute population.
${\text{Absolute population = }}\dfrac{{{\text{given percent}}}}{{100}} \times Total$

Complete step by step solution:
For the given question, the total population in $1998$ is $3276000$.
We need to find the population of U.P. and M.P. in 1998 with the help of the given percentage, in the pie diagram.
Thus, population of U.P in $1998 = {\text{15%   of  327600}}$
Here we have to convert the percentage,
$ \Rightarrow \dfrac{{15}}{{100}} \times 3276000$
On simplification we get,
$ \Rightarrow 491400$
Population of M.P. in 1998= ${\text{20%  of  3276000}}$
We have to convert the percentage,
$ \Rightarrow \dfrac{{20}}{{100}} \times 3276000$
On some simplification we get,
$ \Rightarrow 655200$
Let us consider the population of U.P in 1997 to be X.
There was an increase of \[10\% \] in the population of U.P from 1997 to 1998.
So we can write it as, by using the formula of annual income
$ \Rightarrow X\left( {1 + \dfrac{{10}}{{100}}} \right) = 491400$
Taking LCM on bracket term and we get
$ \Rightarrow X\left( {\dfrac{{110}}{{100}}} \right) = 491400$
Taking X as LHS and remaining as RHS we get,
$ \Rightarrow X = 491400 \times \dfrac{{100}}{{110}}$
On simplify we get
$ \Rightarrow X = 446727.273$
Here we have to write the approximate value of X
$X \approx 446727$
Let us consider the population of M.P. in 1997 is Y. There was an increase of \[12\% \] in the population of M.
So we can write it as, by using the formula of annual increase.
$ \Rightarrow Y\left( {1 + \dfrac{{12}}{{100}}} \right) = 655200$
Taking LCM on bracket term and we get,
$ \Rightarrow Y\left( {\dfrac{{112}}{{100}}} \right) = 655200$
Taking Y as LHS and remaining as RHS we get,
$ \Rightarrow Y = 655200 \times \dfrac{{100}}{{112}}$
On some simplification we get
 $ \Rightarrow Y = 585000$
So, the population of U.P in 1997 was $446727$and the population of M.P. was $731250$
We have to find the ratio of these two states in 1997.
The ratio is $X:Y$
So we can write it as, $446727:585000$
Now we have to write it ratio as division form,
$ \Rightarrow \dfrac{{446727}}{{585000}}$
Let us divide the term and we get
$ \Rightarrow 0.7636$
Hence the population of U.P. and M.P. in $1997$ is $0.7636$
In the question have an option like in the ration form.
So we have to check it as,
Option A says, $42:55$=$\dfrac{{42}}{{55}}$=$0.7636$
Option B says, $48:55$=$\dfrac{{48}}{{55}}$=$0.8727$
Option C says, $7:11$=$\dfrac{7}{{11}}$=$0.6363$
Option D says, $4:5$=$\dfrac{4}{5}$=$0.8$

Hence the correct option is A.

Note: Ratio is the quantitative relationship between two amounts. It shows how many times one number has occurred with respect to the other. Here, we calculated the ratio, that is, both the numbers are commonly divisible by some other number.