Question

The population of a city decreases by 10% at the end of the second year, and if the population of the city at the beginning of the first year again decreases by 10% at the end of the first year and increases by 10% at the end of the third year, making it 4465. Then what was the (l point)?

Options:
a. Initial population of the city.
b. Final population of the city.
c. Percentage increase in population.
d. Percentage decrease in population.

Answer 1

The initial population of the city was 5000.

Step-by-step explanation:

To solve this problem, we need to work backwards. Let's assume the initial population of the city is P.

At the end of the first year, the population decreases by 10%:

P - 0.1P = 0.9P

At the end of the second year, the population decreases by 10% from the population at the end of the first year:

0.9P - 0.1(0.9P) = 0.9P - 0.09P = 0.81P

At the end of the third year, the population increases by 10% from the population at the end of the second year:

0.81P + 0.1(0.81P) = 0.81P + 0.081P = 0.891P

We are given that the population at the end of the third year is 4465:

0.891P = 4465

To find P, we can divide both sides of the equation by 0.891:

P = 4465 / 0.891 = 5000 (rounded to the nearest whole number)

Therefore, the initial population of the city was 5000.