A colony of ants increases its population by 4 percent. If after this

Question

A colony of ants increases its population by 4 percent. If after this increase, bacteria deplete the population by 3/4, the new ant population is what percent of the original ant population?

A. 16%
B. 26%
C. 29%
D. 50%
E. 78%

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Krunaal · Answer

A colony of ants increases its population by 4 percent. If after this increase, bacteria deplete the population by 3434, the new ant population is what percent of the original ant population?

I think there is some mistake with the above question, or given answer choices, or it is worded ambiguously and I'm not able to get it - please let me know  Bunuel

Here's my attempt -

Let original ant population be "x"
It increases by 4% => "1.04x"

Bacteria depletes it by 3434 => "1.04x - 3434"

New ant population = 1.04x -3434

We need to find the new ant population is what percent of the original ant population, let "k" be that percent,
1.04x - 3434 = k*x
1.04 - 3434/x = k
3434/x = 1.04 - k
x = 3434/(1.04 - k)

x has to be an integer as it is ant population, therefore (1.04 - k) needs to be a factor of 3434 => 101*17*2

When we test answer choices for k,

A. (1.04 - 0.16) => 0.88 => 88 is not a factor of 343400;  Incorrect 
B. (1.04 - 0.26) => 0.78 => 78 is not a factor of 343400;  Incorrect 
C. (1.04 - 0.29) => 0.75 => 75 is not a factor of 343400;  Incorrect 
D. (1.04 - 0.50) => 0.54 => 54 is not a factor of 343400;  Incorrect 
E. (1.04 - 0.78) => 0.26 => 26 is not a factor of 343400;  Incorrect

No single answer possible

Bunuel · Answer

You are right. IT should have been 3/4 instead of 3434. Edited. Sorry for the typo.

tgsankar10 · Answer

Ant colony population  - x

Increased by  4	ext{%}=1.04x

\frac{3}{4}  depleted  = 0.75*1.04*x=0.78x

Remaining population  =1.04x-0.78x=0.26x=26	ext{% of }x

Answer is B

Krunaal · Answer

No worries, thank you! Below is my updated solution,

Let original ant population be "x"
It increases by 4% => "1.04x"

Bacteria depletes it by 3/4 => New population would be 1/4th

New ant population = 1/4 * 1.04x

We need to find the new ant population is what percent of the original ant population, let "k" be that percent,
1.04x * 1/4 = k*x
0.26 = k

Therefore,  answer is B. 26%

pierjoejoe · Answer

can't we just say that:

initial population P0 
increase P1 = P0(1+4%)
decrease P2 = P0(1+4%)(1-75%)

thus the population decreases by 
4%-75% - (75*4/100)% = 4% - 75% - (300/100)% = - 71% - 3% = -74%

thus the population decreases by 74% --> the remaining population (P2) is 26% of the original (P0).

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A colony of ants increases its population by 4 percent. If after this

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