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Time and work related

by guerrero » Tue Mar 05, 2013 1:35 am
A can do a piece of work in 10 days, B in 15 days. They work for 5 days. The rest of work finished by C in 2 days. If they get $1500 for the whole work, the daily wages of B and C are how much ?

a)150
b)225
c)250
d)300
e)450


As 1 day work - 1/10
B's 1 day work -1/15

Their 5 day work to gather is = 5/6
Remaining 1/6 work done by c= 2 days
therefore , C's 1 day work is=1/12

Ratio of their efficiency -A:B:C = 6:4:5
Amount to be paid to B and C is = 4/15*1500 + 5/15*1500=400+500
so daily wages of B n C = 400/15 + 500/12--- Where is the mistake ?:(
[spoiler]

OA B[/spoiler]
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by Anurag@Gurome » Tue Mar 05, 2013 1:45 am
guerrero wrote:A can do a piece of work in 10 days, B in 15 days. They work for 5 days. The rest of work finished by C in 2 days. If they get $1500 for the whole work, the daily wages of B and C are how much ?
The money will be distributed on the basis of how much they have contributed, i.e. what fraction of the work they have done NOT on the basis of their work efficiency, i.e. how much work they could've done.

Hence, their daily wage will be (fraction of work they do in one day)*(total money)

Therefore,
  • Daily wage of B = $(1/15)*(1500) = $100
    Daily wage of C = $([(1 - 5/6)/2]*(1500) = $(1500/12) = $125
Hence, the daily wages of B and C = $(100 + 125) = $225

The correct answer is B.
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by GMATGuruNY » Tue Mar 05, 2013 3:42 am
guerrero wrote:A can do a piece of work in 10 days, B in 15 days. They work for 5 days. The rest of work finished by C in 2 days. If they get $1500 for the whole work, the daily wages of B and C are how much ?

a)150
b)225
c)250
d)300
e)450
[spoiler]

OA B[/spoiler]
Let the job = 30 units.

Since A can complete the job in 10 days, A's rate = w/t = 30/10 = 3 units per day.
Since B can complete the job in 15 days, B's rate = w/t = 30/15 = 2 units per day.

Work produced by A in 5 days = r*t = 3*5 = 15 units.
Work produced by B in 5 days = r*t = 2*5 = 10 units.
The remaining work is produced by C:
30-15-10 = 5 units.

Since B produces 10 of the 30 units, B earns 10/30 = 1/3 of the total amount paid:
(1/3)1500 = 500.
Since B works for 5 days, B's daily payrate = 500/5 = $100 per day.

Since C produces 5 of the 30 units, C earns 5/30 = 1/6 of the total amount paid:
(1/6)1500 = 250.
Since C works for 2 days, C's daily payrate = 250/2 = $125 per day.

Sum of the two daily payrates = 100+125 = 225.

The correct answer is B.
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by saurav.jha » Mon Mar 11, 2013 6:59 am
Rate of work done by A in one day 10%
Rate of work done by B in one day 6.67%
Percentage work done together in 1 day 16.67%
Total work done by them in 5 days 16.67 * 5= 83.35%
Work left for C 100-83.35= 16.65%
Total percentage work done by A= 50%
Total percentage work done by B = 6.67*5= 33.35 %
Total percentage work done by C = 16.65%
So ratio of wages shall be in the ratio of the total work done by them 3:2:1
Total of B and C shall be 500 and 250
Daily shall be 500/5 + 250/2 = 100+125= 225 answer
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