Explanation in simple way needed for the given: Arithmetic:

[Divya Ann Chacko]

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

Answer is option E. How this answer can be reached?

[Brent@GMATPrepNow]

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 think the fast way is to plug in some nice numbers.
Since the two pieces of information regarding the night shift are related to the information regarding the day shift, let's assign some nice values to the day shift.

Number of workers
Day shift: 5 workers (this is an easy number to find 4/5 of)
Night shift: 4 workers (4/5 of 5 = 4)

Boxes loaded per worker
Day shift: 4 boxes per worker
Night shift: 3 boxes per worker (3/4 of 4 = 3)

Total boxes loaded
Day shift: 5 workers times 4 boxes per worker = 20 boxes
Night shift: 4 workers times 3 boxes per worker = 12 boxes

COMBINED total boxes for BOTH shifts = 20 + 12 = 32

Of the 32 boxes, the day shift loaded 20 of them.
20/32= 5/8 = E

Cheers,
Brent

[Divya Ann Chacko]

Thank you very much for this simple explanation. I am only confused that how will we think in this simple manner as you did for the GMAT exam.

Thank you very much once again

[Brent@GMATPrepNow]

Notice that the question did not ask us to find the NUMBER of boxes loaded. Instead, it asked us to find a FRACTION.

When a question asks us to find a certain FRACTION, PERCENT or RATIO, we can often plug in numbers that satisfy the given conditions and then use these for our calculations.

Cheers,
Brent

[Divya Ann Chacko]

Ohhh!!...Thats good...!! Thank you very much.

[Mathsbuddy]

N = number of night workers
D = number of day workers = 5N/4

n = number of boxes per night person
d = number of boxes per day person = 4n/3

X = Total number of day boxes = D * d = 20Nn/12
Y = Total number of night boxes = N * n
T = Total overall = X + Y = 32Nn/12

Required Fraction = X/T = 20/32 = 5/8

ANSWER = e) 5/8

[Divya Ann Chacko]

The above two explanations provided two different ways of thinking. Both of these explanations helped me alot to have a different kind of thinking. Thank you very much

[Mathsbuddy]

The above two explanations provided two different ways of thinking. Both of these explanations helped me alot to have a different kind of thinking. Thank you very much

I also like to see a variety of different approached myself
I hope it's clear why I inverted the fractions at the beginning.
If not, it would have worked like this too:

D = number of day workers
N = number of night workers = 4D/5

d = number of boxes per day person
n = number of boxes per night person = 3d/4

X = Total number of day boxes = D * d
Y = Total number of night boxes = 12Dd/20
T = Total overall = X + Y = 32Dd/20

Required Fraction = X/T = 20/32 = 5/8

ANSWER = e) 5/8

[Divya Ann Chacko]

I tried this way. But i was not able to reach the answer. But now i understood it. Thanks alot!!