At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/8

Just take the Box Loaded by each Night crew is Bn and Box Loaded by each Day Crew is Bd.Then
According to question (Bn)=(3/4)(Bd) i.e (Bn)/(Bd)=3/4

Now again let Night Crew Has Nn number of crew members and Day crew has Nd members.Then according to question (Nn)=(4/5)(Nd) i.e (Nn)/(Nd)=4/5

As number of box carried by the group will be the product of Number of crew multiplied by the number of boxes carried by each member,
According to question we need to find out { (Nd)(Bd) } / { (Nn)(Bn)+(Nd)(Bd) }

Dividing the Nominator and denominator by (Nd)(Bd),

We get, 1 / { (Nn)(Bn)/(Nd)(Bd) + 1 } i.e 1 / { (Nn)/(Nd)*(Bn)/(Bd) + 1 }

i.e 1 / { (3/4)*(4/5) + 1} =5/8

So answer is E.
Thanks for a valued Question.

Consider KUDOS if you like the Solution.

night crew loads 3/4 of what day crew loads.

Also, night crew is 4/5th day crew.

Therefore if one day crew member loads x boxes
Night crew is 4/5th of (1 ) * 3/4 = 3/5x

Therefore total number of boxes per crew member (1 night + one day crew) 3/5x +x
= 8/5x.


The x/8/5x = 5/8

Say,
Day crew = 5 people
Night crew = (4/5)*5 = 4 people

Each person in day crew loaded = 4 boxes.
Each person in night crew loaded = (3/4)*4= 3 boxes.

Total boxes loaded by day crew = 5*4 = 20
Total boxes loaded by night crew = 4*3 = 12

Fraction of boxes loaded by day crew = 20/(20+12) = 20/32 = 5/8

Ans: "E"
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Hi,
I'm trying to plug in for Question # 138 in OG 12. Could anyone point out where i'm going wrong in my reasoning? I understand the solutions posted in the earlier posts but would like to know where i went wrong.
No. of Boxes loaded by Night workers = 3/4 of Day workers
No. of Night workers = 4/5 of Day workers.

Let the number of Day workers = 100 and they load a total of 100 boxes.
No. of boxes loaded by Night workers = 3/4 x 100 = 75
No. of Night workers = 4/5 x 100 = 80

total no. of boxes loaded by both workers = 175
total no. of boxes loaded by day workers = 100

fraction of boxes loaded by day workers out of the total = 100/175 = 4/7
The closest answer is 4/5 which is D.

But the correct answer is 5/8 which is E.

Night Crew rate = (3/4)* Day Crew rate. -----------------1

Number of night Crew workers = (4/5)*Day crew workers.-------------2

Total Work done by Day crew workers = Number of day crew workers * day crew worker rate.

Total Work done by Night crew workers = Number of night crew workers * night crew worker rate

= (4/5) Day crew workers * (3/4) * Day crew rate

= (3/5)* Total work done by Day crew workers


fraction of all the boxes loaded by the two crews did the day crew load = 1/(1+(3/5)) = 5/8

Answer is E.

If you don't have the book in front of you the question is:

At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
a. 1/2
b. 2/5
c. 3/5
d. 4/5
e. 5/8

I didn't know how to answer this question so I looked at the answer explanations and I still do not understand how to get the answer. The explanation says:

From this, the workers on the night crew will load 3/4(4/5)= 3/5 as many boxes as the day crew. The total loaded by both the day and night crews is thus 1 + 3/4= 5/5 + 3/5= 8/5 of the day crew's work. Therefore, the fraction of all the boxes loaded by the two crews that was done by the day crew was 1/8/5 = 1(5/8) = 5/8.

I understand the first sentence saying that the night crew will load 3/5 as many boxes as the day crew. Where I get mixed up is in the next sentence, The total loaded by both the day and night crews is thus 1 + 3/5 = 5/5 + 3/5 = 8/5 of the day crew's work. I do not understand where the 1 comes from. I am figuring that the number 1 represents the day crew. Is it saying the night crew loads 3/5 as many as the day crew so the day crew loads 5/5? Can someone please explain this to me??

Thanks,

Josh

At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many worker as the day crew, what fraction of all the boxes loaded by the two crew did the day crew load.

A) 1/2
B) 2/5
C) 3/5
D) 4/5
E) 5/8