CAT 2023 Slot 3 QA Question 11: The population of a town in 2020 was 100000. The population decreased by y% from the year 2020 to 2021, and increased by x% from the year 2021 to 2022, where x and y are two natural numbers. If popula

Question

The population of a town in 2020 was 100000. The population decreased by y% from the year 2020 to 2021, and increased by x% from the year 2021 to 2022, where x and y are two natural numbers. If popula

Accepted Answer

For the 2022 population to be greater than the 2020 population, the increase percentage must exceed the decrease percentage. Hence, $x = y + 10$.

The 2022 population is greater than 100000, so

$100000\left(1 - \dfrac{y}{100}\right)\left(1 + \dfrac{y + 10}{100}\right) > 100000$
$(100 - y)(110 + y)