Question

Population of a city decreases by 10% at the end of first year and increases by 10% at the end of second year and again decreases by 10% at the end of third year. If the population of the city at the end of third year is 4455, then what was the population of the city at the beginning of the first year?

Answer 1

Answer:

5000

Step-by-step explanation:

Starting from last year,

As 4455 is the population after decrease of 10% by last year

So population at last of 2nd year (z)=4455/90 x 100 =4950

Now 4950is the population after increase of 10% by last year

So population at last of 1st year (y)= 4950/110 x 100 =4500

Similarly,

Population in beginning of 1st year (x) = 4500/90 x 100

=5000

Answer 2

Answer:

The population of the city at the beginning of the first year was 5000.

Step-by-step explanation:

We Know, a% of b $= \frac{a}{100} \times b$

By some examples,we can understand this concept.

Example -1:

$5\% \: of \: 50 \\ = \frac{5}{100} \times 50 \\ = \frac{5}{2} \\ = 2.5$

Example -2:

$10\% \: of \: 500 \\ = \frac{10}{100} \times 500 \\ = 10 \times 5 \\ = 50$

Example -3:

$50\% \: of \: 750 \\ = \frac{50}{100} \times 750 \\ = 5 \times 75 \\ = 375$

Let at the beginning of the first year population was x.

Given,Population of a city decreases by 10% at the end of first year.

So now population

$= \frac{100 - 10}{100} \times x \\ = \frac{90}{100} \times x \\ = \frac{9x}{10}$

Again given that at the end of first year and increases by 10%.

So, now population

$= \frac{100 + 10}{100} \times \frac{9x}{10} \\ = \frac{99x}{100}$

Again population decreases by 10% at the end of third year.

So, population now

$= \frac{100 - 10}{100} \times \frac{99x}{100} \\ = \frac{9 \times 99x}{100} \\ = \frac{891x}{1000}$

It is also given that the population of the city at the end of third year is 4455

So, according to question

$\frac{891x}{1000} = 4455 \\ x = \frac{4455 \times 1000}{891} \\ = \frac{405 \times 1000}{81} \\ = 5000$

Therefore, the population of the city at the beginning of the first year was 5000.

This is a problem of percentage.

Know more about percentage:

https://brainly.in/question/10002322

https://brainly.in/question/33820520

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