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

Question

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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chetan2u · Accepted Answer

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%

pushpitkc · Answer

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.

PKN · Answer

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)

praveenkuragodi · Answer

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

chetan2u · Answer

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

GMATGuruNY · Answer

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:

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 %.

D

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

stne · Answer

Worked on the problem assuming they worked in the sequence of their names respectively.

Adam takes 10 days to do whole work, Adam's rate - \frac{1}{10}  and Ben takes 5 days to do whole work, Ben's rate - \frac{1}{5} 
 \frac{1}{10}  +  \frac{1}{5} + \frac{1}{10} + \frac{1}{5} + \frac{1}{10} + \frac{1}{5} + \frac{1}{10}  - since work is completed in 7 days

Total work by Adam in 7 days  \frac{1}{10}  + \frac{1}{10}  + \frac{1}{10}  + \frac{1}{10}  Hence % work  \frac{4}{10}*100  =40%

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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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