Math, asked by alpharex41, 20 days ago

The population of a colony of ants first increased by m% and then decreased by m%. As a result, the population decreased by 1200 compared to the initial population. It again increased by (m/2)% and then decreased by (m/2)%. At this stage, the population was 28,512. Find the initial population.
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A.30000
B.40000
C.25000
D.20000

Answers

Answered by llXxarmygirlxXll

Answer:

The population of a colony of ants first increased by m% and then decreased by m%. As a result, the population decreased by 1200 compared to the initial population. It again increased by (m/2)% and then decreased by (m/2)%. At this stage, the population was 28,512. Find the initial population

Step-by-step explanation:

A.) 30000

Answered by arshikhan8123

Concept:

A ratio or value that may be stated as a fraction of 100 is called a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. It's denoted by the sign "%"

Given:

Find:

Find the initital population

Solution:

Let initial population of ants = 100x .

after increasing M% ,

→ Population of ants = 100x * (100 + M)/100 = x(100 +M) .

and, after decreasing M% ,

→ Present Population of ants = x(100 + M) * (100 - M)/100 = x(10000 - M²)/100 = {100x - (M²x/100)}

then

→ Population of ants decreased by = M²x/100 .

hence,

% decreased in population of ants = (M²x/100) * 100 / (100x) = (M²/100) %

As per question,

M²x/100=1200--------------------(i)

Again,

Again the population increased by m/2% and then idecreased by m/2%

So, present population=100x-M²x/100-M²x/400

=100x-5M²x/400

As per question,

100x-5M²x/40028512

Now, substituting the value of eq (i)

100x-5x1200=28512

100x-6000=28512

100x=34512

Therefore, the initia; population of ants =34512, which can be approximated to 30,000, So optio A is the answer.

#SPJ3

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