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Adam alone can do a piece of work in 15 days and Bart alone can do

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Adam alone can do a piece of work in 15 days and Bart alone can do [#permalink] New post   03 Dec 2020, 21:22
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Adam alone can do a piece of work in 15 days, and Bart alone can do the same work in 10 days. Adam and Bart undertook to do it for $7200. With the help of Charlie, they finished the work in 5 days. How much is paid to Charlie?

A. $720
B. $1200
C. $2250
D. $2400
E. $3000
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Re: Adam alone can do a piece of work in 15 days and Bart alone can do [#permalink] New post   24 Mar 2021, 18:22
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Adam alone can do a piece of work in 15 days, and Bart alone can do the same work in 10 days. Adam and Bart undertook to do it for $7200. With the help of Charlie, they finished the work in 5 days. How much is paid to Charlie?

Adam rate=\(\frac{1}{15}\) of the work per day
Bart rate=\(\frac{1}{10}\) of the work per day
A+B+C rate=\(\frac{1}{5}\) of the work per day
What is Cs per day rate?
\(\frac{1}{5}-\frac{1}{10}-\frac{1}{15}=\frac{1}{30}\)

C works for 5 days. \(Work=Rate·Time=\frac{1}{30}·5=\frac{1}{6}\). C deserves 1/6th of the money
$7200·1/6=$1200
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Adam alone can do a piece of work in 15 days and Bart alone can do [#permalink] New post   03 Dec 2020, 22:01
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CONCEPT:-Time and Work
-Wage is calculated by calculating the total work done in 5 days by each

SOLUTION: Work done in 5 days by Adam=(1/15)*5=1/3
Amount that Adam gets= (1/15)*5*7200=2400$
Amount that Bart gets=(1/10)*5*7200=3600$
Hence amount that Charlie gets=7200-(2400+3600)=1200$(B)

Hope this helps :thumbsup:
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Re: Adam alone can do a piece of work in 15 days and Bart alone can do [#permalink] New post   03 Dec 2020, 22:03
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Adam and Bart can complete 16.66% of the task in a day.
(As Adam can complete 6.66% task a day
Bart can complete 10% of the task a day)
When Charlie joins, they complete 20% task a day

So Charlie's contribution is 3.33%
So he should be paid 3.33/20 *7200
= 10/3*360= 1200

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Re: Adam alone can do a piece of work in 15 days and Bart alone can do [#permalink] New post   03 Dec 2020, 22:41
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Explanation:

Adam alone can do a piece of work in 15 days
Bart alone can do the same work in 10 days.
Both Adam & Bart One day work = 1/15 + 1/10 = 2+3/30 = 1/6 i.e. 6 days to complete work
If charlie also joined Adam & Bart in work, then work is completed in 5 days.
1/A + 1/B + 1/C = 1/5
1/6 + 1/C = 1/5
1/C = 1/5 - 1/6
1/C = 1/30

Charlie alone can do work in 30 days.

Ratio of per day work between all 3 = 1/15: 1/10:1/30
1/3:1/2:1/6

Money divided in ratio = 6*(1/3:1/2:1/6) = 2:3:1

Adam and Bart undertook to do it for $7200.

So charlie share = 1/6 x 7200 = 1200$

IMO-B
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Re: Adam alone can do a piece of work in 15 days and Bart alone can do [#permalink]
03 Dec 2020, 22:41
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