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?

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 2)
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Answer (Detailed Solution Below)

Option 1 :
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SSC CGL Tier 1 2025 Full Test - 01
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Detailed Solution

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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

Now, % decrease

∴ The percentage decrease in 'x' from 2020 to 2021 is .

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,

  2020 2021
A 200 160
B 100 90

So now,

x = 2 and x' = 16/9

now as per the question,

× 100 ⇒ (100/9)

Now substituting the values in the given options,

Only 1 option satisfies the value.

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