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If Adam can do a job in 10 days and Ben's speed is twice of Adam's spe

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If Adam can do a job in 10 days and Ben's speed is twice of Adam's spe  [#permalink]

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New post 04 Jul 2018, 21:52
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If Adam can do a job in 10 days and Ben's speed is twice of Adam's speed and both work one after another, what % of the work should be done by Adam to complete the work in exact 7 days?
(A) 67%
(B) 60%
(C) 50%
(D) 40%
(E) 33%


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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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If Adam can do a job in 10 days and Ben's speed is twice of Adam's spe  [#permalink]

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New post 04 Jul 2018, 22:25
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chetan2u wrote:
If Adam can do a job in 10 days and Ben's speed is twice of Adam's speed and both work one after another, what % of the work should be done by Adam to complete the work in exact 7 days?
(A) 67%
(B) 60%
(C) 50%
(D) 40%
(E) 33%


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Doesn't matter in what sequence or pattern they work, we are interested in the % of work completed in the end of 7 days.
And to finish the work in 7 days, only one solution is possible


The shortest method..

1) weighted average method

So if works can be completed in 5 and 10 days and we are looking for 7 days
5--7---10
So Adam who does in 10 days will do \(\frac{7-5}{10-5}=\frac{2}{5}\) of the work and 2/5 in % = \(100*\frac{2}{5}=40%\)

2) work/rate problem

Let A works for x days, and his x day work will be \(\frac{x}{10}\)
so B will work for 7-x days, and his 7-x days work \(=\frac{(7-x)}{5}\)

\(\frac{x}{10} + \frac{(7-x)}{5} = 1.........x+14-2x=10......x=4\)
So A works for 4 days in total .....% of work completed in 3 days =\(100*\frac{4}{10}=40%\)
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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If Adam can do a job in 10 days and Ben's speed is twice of Adam's spe  [#permalink]

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New post 04 Jul 2018, 22:42
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chetan2u wrote:
If Adam can do a job in 10 days and Ben's speed is twice of Adam's speed and both work one after another, what % of the work should be done by Adam to complete the work in exact 7 days?
(A) 67%
(B) 60%
(C) 50%
(D) 40%
(E) 33%


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Adam does the work in 10 days and since Ben's speed is twice Adam's speed,
Ben does the same job in 5 days. Let's assume the total work to be 100 units.

Now, the individual rates are Adam - 10 units/day and Ben - 20 units/day.

We need to find how much work does Adam need to do such that the work is completed in
7 days. If \(x\) is the number of days Adam works, then \(7-x\) is the number of days Ben works

\(10x + 20(7-x) = 100\) -> \(10x + 140 - 20x = 100\) -> \(10x = 40\) -> \(x = \frac{40}{10} = 4\)

Therefore, Adam does \(40(4*10)\) units of the total \(100\) units, which is \(\frac{40}{100} = 40\)% (Option D) of the work.
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Re: If Adam can do a job in 10 days and Ben's speed is twice of Adam's spe  [#permalink]

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New post 04 Jul 2018, 23:06
chetan2u wrote:
If Adam can do a job in 10 days and Ben's speed is twice of Adam's speed and both work one after another, what % of the work should be done by Adam to complete the work in exact 7 days?
(A) 67%
(B) 60%
(C) 50%
(D) 40%
(E) 33%


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Question stem, \(\frac{W_{A}}{W_{Total}}\)*100=?

Given, \(r_{A}\)=\(\frac{1}{10}\) & \(r_{B}\)=2*\(\frac{1}{10}\)=\(\frac{1}{5}\)
\(t_A+t_B=7\)

We know, work=Rate*Time & Total work done=1

So, \(r_A*t_A+r_B*t_B=1\)
Or, \(\frac{1}{10}*t_A+\frac{1}{5}*(7-t_A)=1\)
Or, \(14-t_A=10\)
Or, \(t_A=4\)

Now, \(\frac{W_{A}}{W_{Total}}\)*100=\(\frac{r_A*t_A}{1}\)*100=\(\frac{1}{10}\)*4*100=40%

Ans. (D)
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Re: If Adam can do a job in 10 days and Ben's speed is twice of Adam's spe  [#permalink]

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New post 05 Jul 2018, 01:58
chetan2u wrote:
If Adam can do a job in 10 days and Ben's speed is twice of Adam's speed and both work one after another, what % of the work should be done by Adam to complete the work in exact 7 days?
(A) 67%
(B) 60%
(C) 50%
(D) 40%
(E) 33%


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Both work one after another??? both work one after another for 1 day each or 2 day each?? no clarity
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Re: If Adam can do a job in 10 days and Ben's speed is twice of Adam's spe  [#permalink]

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New post 05 Jul 2018, 02:05
praveenkuragodi wrote:
chetan2u wrote:
If Adam can do a job in 10 days and Ben's speed is twice of Adam's speed and both work one after another, what % of the work should be done by Adam to complete the work in exact 7 days?
(A) 67%
(B) 60%
(C) 50%
(D) 40%
(E) 33%


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Both work one after another??? both work one after another for 1 day each or 2 day each?? no clarity



That doesn't matter at all..
Since we have to ensure that the work has to be completed in 7 days and both have different speed, IT is possible only if they do certain% of work ..
The answer will not change if A works for 10 h and then B works for 1hr or there is NO pattern in their working. Finally the work jaa to be completed in exact 7 daya
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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If Adam can do a job in 10 days and Ben's speed is twice of Adam's spe  [#permalink]

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New post 05 Jul 2018, 02:35
Quote:
both work one after another


A reasonable test-taker might interpret this information as follows:
If Adam works one day, then Ben must work the next day.
Earlier posts suggest that a different interpretation is intended.
I believe that the following clarifies the intent of the problem:

Quote:
Adam can do a job in 10 workdays. Ben's speed is twice Adam's speed. Every workday either Adam or Ben works but not both. If the job in completed in exactly 7 workdays, what percent of the job is produced by Adam?

(A) 67%
(B) 60%
(C) 50%
(D) 40%
(E) 33%


Let the job = 10 units.
Since Adam takes 10 days to complete the 10-unit job, Adam's rate = \(\frac{w}{t} = \frac{10}{10} = 1\) unit per day.
Since Ben is twice as fast as Adam, Ben's rate = 2 units per day.
For the 10-unit job to be completed in exactly 7 days, only one case is possible:
Adam works at his rate of 1 unit per day for 4 days, producing a total of 4 units.
Ben works at his rate of 2 units per day for 3 days, producing a total of 6 units.
Thus:
\(\frac{Work-by-Adam}{Total-work} = \frac{4}{10} = 40\)%.



An algebraic way to determine the number of days worked by Adam:
Let \(a=\) Adam's number of days and \(b=\) Ben's number of days.
Since Adam produces 1 unit per day, Ben produces 2 units per day, and a total of 10 units are produced, we get:
\(a+2b=10\)
Since a total of 7 days are worked, we get:
\(a+b=7\)
\(2a+2b=14\)
Subtracting the red equation from the blue equation, we get:
\((2a+2b)-(a+2b) = 14-10\)
\(a=4\)
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