The population of country A decreased by p% and the population of country B decreased by q% from the year 2020 to 2021. Here 'p' is greater than ‘q’. Let 'x' be the ratio of the population of country A to the population of country B in the given year. What is the percentage decrease in 'x' from 2020 to 2021?

Given:

The population of country A decreased by p% and the population of country B decreased by q% from the year 2020 to 2021. Here 'p' is greater than ‘q’. Let 'x' be the ratio of the population of country A to the population of country B in the given year.

Calculation:

Let the initial population of Country A and B be J and K respectively.

Hence, x = J/K

Let the ratio of the population of country A to the population of country B for the next year be x₁.

​According to the question,

(J × (1 - p%)) : (K × (1 - q%)) = x₁

⇒ \(​\frac {J}{K} \times \frac {100 - p}{100 - q} = x_1\)

Now, % decrease

⇒ \(\frac {x - x_1}{x} \times 100\%\)

⇒ \(\frac {\frac {J}{K} - ​\frac {J}{K} \times \frac {100 - p}{100 - q}}{​\frac {J}{K} } \times 100\%\)

⇒ \(\frac {(p - q)}{(100 - q)} \times 100\%\)

⇒ \(\frac{100(p - q)}{(100 - q)} \%\)

∴ The percentage decrease in 'x' from 2020 to 2021 is \(\frac{100(p - q)}{(100 - q)} \%\).

Shortcut Trick

Assume,

The population of A in 2020 be 200 and B in 2020 be 100,

and p = 20% & q = 10% (as per the question)

hence according to the question,

So now,

x = 2 and x' = 16/9

now as per the question,

⇒ \({{2} - {16\over 9}}\over 2\) × 100 ⇒ (100/9)

Now substituting the values in the given options,

Only 1 option satisfies the value.