In a certain egg-processing plant, every egg must be inspect

Question

In a certain egg-processing plant, every egg must be inspected, and is either accepted for processing or rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1. How many eggs does the plant process per day?

(A) 100
(B) 300
(C) 400
(D) 3,000
(E) 4,000

(A) 100
(B) 300
(C) 400
(D) 3,000
(E) 4,000

KarishmaB · Accepted Answer

There is a small ambiguity/typo in this question. I will point it out while solving using ratios:

Usually, Accepted:Rejected = 96:4
That day, Accepted:Rejected = 99:1 (Number of eggs inspected same)
Note that, that day, on the ratio scale, 3 additional eggs were accepted and not rejected. These 3 actually account for 12 additional eggs accepted. So the multiplier is 4 because 3*4 = 12.
Hence total number of eggs inspected = (99+1)*4 = 400

Note here that the question asks you "How many eggs does the plant  process  per day?"
The question uses the word process here: "For every 96 eggs  accepted for processing ..."
So it implies that the number of eggs processed usually is 96*4 = 384 but that is not there in the options. So I assume the question meant to say "how many eggs are inspected per day?"

WoundedTiger · Answer

Thank you for sharing your method.
Could you please tell me how you were able to 'see' the results of the ratio so easily/fast? I mean the 384 and 16 to 24:1, same with the 396 and 4 to 99:1.

384/16 if you divide will give you a ratio of 24:1...like wise 99:1---Multiply both sides by 4 and you get 396:4....

I won't say I am great with tables...but this could be spotted easily....check out the below method using equations...

How about an equation approach?

Let the Total no of. processed egg each day be T and Total of rejected eggs be Y

So T-Y is total no. accepted eggs.

As per question

\frac{T-Y}{Y} =96/4 or 24/1-----> Re arrange the equation and you get

T-Y=24Y or T=25Y

After processing 12 more eggs but keeping the total no. of processed eggs T same, the new eqaution becomes

\frac{T-Y+12}{Y-12} =99/1 ------Rearrange and you get an eqaution
75Y=100*12 or Y=16.

T=25Y so T=25*16=400

Ans is C

Come to think of it, 12 eggs represent nothing but increase in one qty and decrease in another. When total qty produced is same then this change in qty can be indicated as a percentage of Total production.

3%of T=12 or T=400....We can get answer straight away.

WoundedTiger · Answer

Straight pluggin in for me. As usual, I started with C and got the answer.

Lets' back calculate and see what we get

Let us consider eggs processed each day to be 400

So Initial ratio of eggs processed and rejected is 96:4 or 24:1

So out of 400 eggs, there will be 384 eggs processed and 16 rejected.

Now if the no. of eggs inspected remain and 12 more eggs get accepted that means there 384+12=396 eggs accepted and 4 rejected...and the ratio will be 99:1

Bingo...this is what the questions says....

Its always a good idea to start with C.

Saabs · Answer

Thank you for sharing your method.
Could you please tell me how you were able to 'see' the results of the ratio so easily/fast? I mean the 384 and 16 to 24:1, same with the 396 and 4 to 99:1.

ronr34 · Answer

How about an equation approach?

ronr34 · Answer

I tried solving it with this equation but to no success...
Can someone help?

We have : (96X+12)/(4X-12) = 99/1
Solving gets X = 2/5....
I don't get what's wrong....
HELP?

rohitmanglik · Answer

I guess some calculation error. From this equation you will get X= 4.

Put that value back 96 *4 + 4*4 = 400.

desaichinmay22 · Answer

Change in accepted eggs = 12 eggs
Change in % of accepted eggs = 3% (99%-96%)
Therefore eggs per % = 12/3= 4
Therefore total eggs = 4*100=400

1%=4 eggs can also be verified with number of rejected eggs. When 12 fewer eggs are rejected, % of rejection should go down by 12/4= 3% and it is indeed going down by 3% (4%-1%).

Ans = C

PareshGmat · Answer

Inspected ........................... Accepted ............................ Rejected

=96x+4x = 100x ............................ 96x .......................... 4x (Let x be the egg procurement variable)

25x ........................................ 24x ...................................... x (Removing the common factor 4)

25x ......................................... 24x+12 ............................... x-12

If 12 more are accepted, it means "12 less" are rejected

Given that  \frac{24x+12}{x-12} = \frac{99}{1}

99(x-12) = 12(2x+1)

33(x-12) = 4(2x+1)

33x - 33*12 = 8x + 4

25x = 33*12 + 4

25x = 4(33*3 + 1)

x = 4 * \frac{100}{25} = 16

Total eggs = 25*16 = 400

Answer = C

pacifist85 · Answer

This is what I did, but it was only after a long time. So, no way I would have solved it correctly.

Initially: A/R=96/4
Then:A/R=99/1

From 96 to 99 we have a difference of 3.  
From initial number of eggs to latter we have 12 more.  
From   and   we have that this difference of 3 in actual terms is 12 eggs.

So:
3 is 12 eggs
1 is 4 eggs, just cross multiplying 1-->12 | x-->4, which leads to 3x=12 and x=4.

Adding these up:
3 is 12 eggs
1 is 4 eggs
4 is 12 eggs  
100 is x eggs?

Cross multiplying leads to 4x=16(100) | x=1600/4 | x=400.

pacifist85 · Answer

One typo above:

4 is 12 eggs  
100 is x eggs?  
4 is 12 eggs   -------> 4 is 16 eggs

generis · Answer

For some multiplier x, original ratio is

\frac{Accepted}{Rejected}  =  \frac{96x}{4x}

When 12 additional eggs are accepted, total number of eggs does not change but ratio becomes  \frac{99}{1}

\frac{96x + 12}{4x -12}  =  \frac{99}{1}

96x + 12 = 396x - 1188

1200 = 300x

x = 4

From original ratio, total # of eggs processed is

(96)*(4) + (4)*(4) =
384 + 16 = 400

Answer C

Cw007 · Answer

I come to the right solution with a very simple approach, any feedback to this?

x= accepted eggs

x*0.96+12=x*0.99 --> x= 12/0.03=  400 ,  (C)  is correct

bumpbot · Answer

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In a certain egg-processing plant, every egg must be inspect

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