X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. If 40% of the total work is done by X, for how many days did X and Y work together?
A. 2
B. 3
C. 4
D. 5
E. 6
The OA is B.
I don't have clear this PS question. I appreciate if any expert explains it to me. Thank you so much.
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X takes 10 days to complete a task. Y takes half that...
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GMATGuruNY
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Let the task = 100 units.AAPL wrote:X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. If 40% of the total work is done by X, for how many days did X and Y work together?
A. 2
B. 3
C. 4
D. 5
E. 6
Since Y's time is 1/2 X's time -- and X's time is 10 days -- Y's time to complete the 100-unit task is 5 days.
Thus, Y's rate = w/t = 100/5 = 20 units per day.
Since X produces 40% of the 100 units -- for a total of 40 units -- Y produces the remaining 60 units.
Since Y's rate = 20 units per day, the time for Y to produce 60 units = w/r = 60/20 = 3 days.
The correct answer is B.
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Jeff@TargetTestPrep
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We can let the number of days X worked alone = x and the number of days X and Y worked together = t. Since the rate of X is 1/10 and the rate of Y is 1/5, we have:AAPL wrote:X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. If 40% of the total work is done by X, for how many days did X and Y work together?
A. 2
B. 3
C. 4
D. 5
E. 6
x(1/10) + t(1/10) = 2/5
and
x(1/10) + t(1/10 + 1/5) = 1
If we subtract the first equation from the second, we have:
t(1/5) = 3/5
t = 3
Answer: B
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