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Rational Number

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Rational Number

by samsachd » Mon Aug 10, 2009 4:23 am
Q: At a Docking Station,each worker on night crew loaded 3/4 as many as boxes as each worker on the day crew.If the night crew has 4/5 as many as workers as day crew then 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 am not able to understand the reasoning given for this Ques. in OG11?
Can anyone put more info on this.
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here's what it looks like to me...

by qbert » Mon Aug 10, 2009 6:27 am
i don't know what OG11 is, but when i read this question, i think it helps to plug in numbers.

day crew = 100 people
night crew = 4/5d = 80 people

day crew rate = 4 boxes
night crew rate = 3/4d = 3 boxes

100 day crew people * 4 boxes = 400 boxes
80 night crew people * 3 boxes = 240 boxes

day / total = day / day + night = 400 / (400+240) = 5 / 8 = answer E.
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Alternative method

by enniguy » Tue Aug 11, 2009 1:28 am
Alternatively, you can solve it this way.
Consider they hardly loaded any box. Also ignore 4/5 person. (Just take it for calculation)

Day Crew: 1 Person loaded 1 box.
Night Crew: 4/5 Person loaded 3/4 box.

Total Boxes loaded by Day crew = 1*1 = 1
Total Boxes loaded by Night crew = (4/5)*(3/4) = (3/5)
Grand total of boxes loaded = 1 + (3/5) = 8/5

Boxes by Day Crew / Total boxes loaded = 1 / (8/5)

= 5/8.

--E
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Sol'n

by samsachd » Tue Aug 11, 2009 3:46 am
Thanks!!!!
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by sreak1089 » Wed Aug 12, 2009 3:56 am
I prefer algebraic way of doing it:

Day crew --> x*n (x boxes, n persons)
Night crew --> 3x/4 * 4n/5 (3/4 (x) boxes, 4/5(n) persons) = 3/5 (x*n)
Total --> 8/5 (x*n)
Day crew frachtion = x*n / (8/5 * (x*n)) == 5/8 Hence E.
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