Question
Download Solution PDFThe 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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,
⇒
Now substituting the values in the given options,
Only 1 option satisfies the value.
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