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If 20% of certain quantity of work is done by...

by swerve » Tue Dec 12, 2017 1:27 pm
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

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
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by Jay@ManhattanReview » Tue Dec 12, 2017 9:23 pm
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

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
Say A does the complete work in a days, thus A takes a/5 days to complete 20% of the work and would take 4a/5 days to complete 80% of the work.
Similarly, say B does the complete work in b days, thus B takes b/5 days to complete 20% of the work and would take 4b/5 days to complete 80% of the work.

Condition 1: 20% of a certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days.

=> a/5 + 4b/5 = 20
a + 4b = 100 ---(1)

Condition 2: 20% of a certain quantity of work is done by B and the rest 80% by A, the work is completed in 30 days.

=> 4a/5 + b/5 = 30
4a + b = 150 ---(2)

Solving (1) and (2), we get a = 100/3 days and b = 50/3 days

A's one-day work = 3/100 and B's one-day work = 3/50

Thus, A and B's one-day work (combined) = 3/100 + 3/50 = 9/100

Thus, A and B together complete (9/100)th part of the work in one day, thus they would take 100/9 = 11 1/9 days to complete the work.

The correct answer: A

Hope this helps!

-Jay
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by GMATWisdom » Wed Dec 13, 2017 5:16 am
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

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
i could not find any short cut method to select the option so we can solve it in the following way

If A independently completes the work in x days
and B independently completes the work in Y days
then 0.2x + 0.8y = 20.....first eqn
And 0.8x + 0.2y = 30........second eqn.
Adding the equations we get x+y =50......third eqn
And subtracting first equation from second we get
0.6(x-y)=10
=> x - y = 10/.6 = 100/6 = 50/3........fourth eqn.
We obtain x*y using third and fourth equation and the formula
X*Y = ¼ [(x+y)^2 - (x - y)^2] = ¼{ 50^2 - (50/3)^2}
=(2500/4)*(1- 1/9) = 5000/9
Together they will complete in xy/(x+y) days
=(5000/9)/ 50 = 100/9 =11 1/9
Hence option A is correct
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by GMATGuruNY » Wed Dec 13, 2017 10:18 am
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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