At a food processing and packaging plant, identical packets of confect

Question

At a food processing and packaging plant, identical packets of confectionary items are prepared at a constant rate by a packaging machine. Each packet contains 3 chocolates, 4 candied nuts and 2 chewing gums. The production rate of chocolates, candied nuts and chewing gums at the plant is 750, 975 and 575 units per hour respectively. All the produced items are immediately sent to a common quality checking machine that can process 3000 units of confectionary items per hour. 20 percent each of chocolates, candied nuts and chewing gums fail the quality check. The remaining items are sent to the packaging plant without any holdup or delay. Which of the following can represent the number of packets of confectionary items prepared by the packaging machine in one hour?

I. 195
II. 230
III. 280

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

I. 195
II. 230
III. 280

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

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NKJJ1990 · Answer

The number of items/pack:
3 Chocolates, 4 Nuts, 2 Gums

The production rates are:
750 Chocolate, 975 Nuts, 575 Gums

Rejection rate = 20%; therefore 80% can be packed:
600 Chocolates, 790 Nuts, 460 Gums

Divide this by the number of items/pack
600/3 = 200, 790/4 = 197.XX, 575/2 = 28Y.YY

The limiting factor is Nuts, therefore the number of packs produced per hour is less than or equal to 197.

Only I is possible.

Answer - A

jain3120 · Answer

Each pack contains - 3 chocolates, 4 candied nuts and 2 chewing gums
No. of items made every hour - 750 chocolates, 975 candied nuts and 575 chewing gums 
Total items made every hour = 750 + 975 + 575 = 2300
Since Quality Check Machine can check upto 3000 items in an hour, it can check our entire batch
No. of items that pass quality check = 80% of items sent in = 600 chocolates, 780 candied nuts and 460 chewing gums

Here comes the tricky part, we will first find out the limiting reagent, that is the max number of packs that can be built.
Let's say all chocolates are packed, therefore no. of packets = 600/3 = 200
For there to be 200 packets, there needs to be sufficient number of other items i.e 200* 4 = 800 candied nuts, however only 780 candied items are available. This rules out any number of packets more than 200.

Since there isn't an option where no option is correct, it is safe to say 195 packets is possible and correct answer is A

hacorus · Answer

This is a long question to calculate with the following method (took me 3min with the online whiteboard), so there must be a better way.

Packages:
3C
4N
2G

Production:
750C
975N
575G
Total<3000 (no need to calculate as all of the terms are less than 1000) so the checking machine can handle it all.

Quality products = 80%
750-75*2=675
975-97-98=975-100-95=780
575-57-58=575-60-55=460

In packages this gives
675/3=225
780/4=195 we can stop here, this is the lowest possible answer choice.

Solution is A I only 195

Lipun · Answer

Ratio in each packet = C:N:G = 3:4:2
Production ratio = C:N:G = 750:975:575

Comparing all 3, we can find out 'N' is the limiting factor (there won't be sufficient quantity of N(975) for the respective quantities of C(750) and G(575)).
Max packets that can be produced =  \frac{975}{4}

No. of packets that pass quality check = 80% of  \frac{975}{4}  =  \frac{4}{5}*\frac{975}{4}  = 195.

Ans: A

ScottTargetTestPrep · Answer

Solution:

Let’s analyze each Roman numeral:

I. 195 packets prepared

If 195 packets were prepared, then 195 x 3 = 585 chocolates, 195 x 4 = 780 candied nuts and 195 x 2 = 390 chewing gums were sent to the packaging machine. This means that 585/0.8 ≈ 731 chocolates, 780/0.8 = 975 candied nuts and 390/0,8 ≈ 488 chewing gums were sent to the quality checking machine. Notice that since 731 + 975 + 488 = 2194 is less than 3000, the quality checking machine is able to process all the confectionary items within the hour. Further, notice that the number of chocolates, number of candied nuts and the number of chewing gums produced in one hour (which are 731, 975 and 488, respectively) are all within the limits of the production rate for each item (which are 750, 975 and 575, respectively). Thus, it is possible that 195 packets were produced.

II. 230 packets prepared

Preparing 230 packets would require 230 x 3 = 690 chocolates passing the quality check; which in turn would require producing 690/0.8 ≈ 862 chocolates per hour. Since the plant can only produce 750 chocolates per hour, preparing 230 packets is not possible.

III. 280 packets prepared

We already know that the plant does not produce chocolates fast enough to prepare 230 packets and preparing 280 packets would require even more chocolates. Thus, without further calculations, we can conclude that the plant cannot produce 280 packets either.

Answer: A

veron90 · Answer

Hi,

Is this also the right way of solving this :

Each packet contains : 3 Choc + 4 Nuts + 2 Candied Gum = 9 per packet

Number of Chocolates, Nuts and Candied Gum produced = 750 + 975 + 575 = 2300

Thus, 80% of 2300 = 1840 (20% rejected)

Hence,  Total packets per hour = 1840/9 = 204 (approx.)

So as per the answer choices,  195  is the only viable option.

Is this flawed, or correct - would appreciate input...thanks! Because it appears that the question is asking  how many units the packaging machine can pack in an hour .

Varun

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At a food processing and packaging plant, identical packets of confect

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