At the moment there are 54,210 tagged birds in a certain wildlife

Question

At the moment there are 54,210 tagged birds in a certain wildlife refuge. If exactly 20 percent of all birds in the refuge are tagged, what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged?

25
30
33 1/3
37 1/2
50

25
30
33 1/3
37 1/2
50

KarishmaB · Accepted Answer

Most percentage questions can be easily solved by assuming values, especially in case the answer is also a percentage.
If there are 100 birds, 20% are tagged so 20 are tagged.
Out of the rest 80, 30 should be tagged so that a total of 50% are tagged.
30/80 = 37.5%

(The huge number given is superfluous, just to make you waste your precious time. Read the question again to realize that it is not needed.)

Ellipse · Answer

All birds = 54210
Currently Tagged = 54210 * 20/100 = 10842
So Untagged birds = 54210 - 10842 = 43368

Half of all birds = 27105
The number of birds to be tagged to make half of all birds tagged = 27105 - 10842 = 16263
So now the question remains - 16263 is how much percentage of untagged birds (43368)
 = 16263 * 100 /43368
 = 37.5 %
Answer (D)

shrive555 · Answer

lengthy calculation ...

krushna · Answer

let x% of remaining birds will be tagged to increase the tagged percentage from 20 to 50

so x% * 80%= 30% hence x = 30 * 5/4 = 37.5

AtifS · Answer

Thank you! Karishma for such an easy solution & the tip

Sarang · Answer

Best answer Karishma!!!

aalriy · Answer

I approached this question as follows:

you have 20% birds tagged and to have 50% birds tagged you need to tag 30% more birds. The question is asking you how much is 30% of the the Currently untagged birds(i.e. 80%)?

So the question is what is (30/80)*100. ~ 40 and the closest option is D.

I totally agree with Karishma that the huge number is superflous and even i did waste my 30 sec on it.

jhagege · Answer

Thanks, this is a clear explanation.
I noticed you often recommend the "weighted average" / alligation method. 
Is it a case where we could have used it as well ? 
When is it preferable to go percentage way vs alligation ?

siddhantvarma · Answer

Karishma's solution is probably the most time-efficient way to solve this question.

However, for those who feel the calculation is length, it isn't. 
Let x: Total number of birds
Tagged = 54210
20 % of x = 54210 => x = 54210*(100/20) => 54210*5  (Don't multiply this yet) 
So now we know that total number of birds: 54210*5

Untagged birds = Total - tagged => 54210*5 - 54210 => 54210*4  (Again, don't multiply this yet) 
We need to know what % of untagged birds must be tagged so overall 50% of the birds are tagged
Which translates to:
y % of untagged + tagged = 50 % of Total
 
Let's plugin the values:
(y/100)*54210*4 + 54210 = (54210*5)/2

As you can see, 54210 can be easily cancelled from the entire equation and now we're left with:

(y/100)*4 + 1 = 5/2
4*y/100 = 3/2 
y = 300/8 => 150/4 => 75/2 => 37.5

Therefore, 37.5% (D)

No lengthy calculations were needed even if you approach the problem traditionally. It took me 1min 20 seconds to solve it this way.

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At the moment there are 54,210 tagged birds in a certain wildlife

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