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
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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

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:
\(\frac{Work-by-Adam}{Total-work} = \frac{4}{10} = 40\)%.



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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