swerve wrote:If 20% os certain quantity of work is done by A the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work, if A and B work together?
A. 11 1/9
B. 10 1/9
C. 12
D. 15
Let A = A's rate, B = B's rate, and the job = 5 widgets.
If 20% of certain quantity of work is done by A the remaining 80% by B, the work is completed in 20 days.
To produce 20% of the 5 widgets -- in other words, to produce 1 widget -- A's time = w/r = 1/A.
To produce the remaining 4 widgets, B's time = w/r = 4/B.
Since the total time is 20 days, we get:
1/A + 4/B = 20.
If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days.
To produce 80% of the 5 widgets -- in other words, to produce 4 widgets -- A's time = w/r = 4/A.
To produce the remaining 1 widget, B's time = w/r = 1/B.
Since the total time is 30 days, we get:
4/A + 1/B = 30.
If we multiply the red equation by 4 to get
4/A + 16/B = 80 and subtract the blue equation, we get:
(4/A + 16/B) -
(4/A + 1/B) =
80-
30
15/B = 50
B/15 = 1/50
B = 15/50 = 3/10 widget per day.
Substituting B = 3/10 into the blue equation, we get:
4/A + 1/(3/10) = 30
4/A + 10/3 = 30
4/A = 80/3
A/4 = 3/80
A = 12/80 = 3/20 widget per day.
Combined rate for A+B = 3/20 + 3/10 = 3/20 + 6/20 = 9/20 widget per day.
Since their combined rate = 9/20 widget per day, the time for A and B together to complete the 5-widget job = w/r = 5/(9/20) = 100/9 = 11 1/9 days.
The correct answer is
A.
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