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# If 20% of certain quantity of work is done by A and the rest by B,

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Intern
Joined: 03 May 2016
Posts: 6
If 20% of certain quantity of work is done by A and the rest by B,  [#permalink]

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18 May 2016, 08:42
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Difficulty:

95% (hard)

Question Stats:

27% (03:08) correct 73% (02:48) wrong based on 150 sessions

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If 20% of certain quantity of work is done by A and 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

Source: TIME material.
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Posts: 9996
Location: Pune, India
Re: If 20% of certain quantity of work is done by A and the rest by B,  [#permalink]

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18 May 2016, 21:41
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Alex75PAris wrote:
Hello Karishma

Can you please explain how you get this : "0.2/A + 0.8/B = 20" ?

Thanks,

Alex

Using the formula: Work = Rate * Time
Time = Work/Rate

Assume A's rate of work is A.
Assume B's rate of work is B.

A does 20% of the work. So if work is 1, A did .2 of the work.

Days for which A worked + Days for which B worked = Total Days (since they work successively)

Work of A/Rate of A + Work of B/Rate of B = Total Days

.2/A + .8/B = 20
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Karishma
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Re: If 20% of certain quantity of work is done by A and the rest by B,  [#permalink]

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18 May 2016, 09:44
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Mohammed22Abrar wrote:
If 20% of certain quantity of work is done by A and 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

Source: TIME material.

Use algebra:

0.2/A + 0.8/B = 20
1/A + 4/B = 100

0.8/A + 0.2/B = 30
4/A+ 1/B = 150

15/B = 250
B = 3/50 work per day
A = 3/100 work per day

Combined rate = 3/40 + 3/100 = 9/100
Time taken when working together = 100/9 = 11(1/9) days

It is not a GMAT type question. For GMAT, it's best to stick to GMAT material.
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Karishma
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Re: If 20% of certain quantity of work is done by A and the rest by B,  [#permalink]

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18 May 2016, 10:40
Hello Karishma

Can you please explain how you get this : "0.2/A + 0.8/B = 20" ?

Thanks,

Alex
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GMAT 1: 660 Q47 V33
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Re: If 20% of certain quantity of work is done by A and the rest by B,  [#permalink]

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20 May 2016, 15:53
Thank you ! it's clear now
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Re: If 20% of certain quantity of work is done by A and the rest by B,  [#permalink]

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05 Jul 2016, 16:47
1
Would anyone be willing to explain why my method didn't work, and why I got a wrong answer?

Eq #1: 0.8 = B *20
Eq #3: 0.8 = A* 30

Solve Eq #1: B = 1/25 = 3/75 using 75 as a common denominator
Solve Eq #2: A = 2/75

Combined rate is 5/75. At a rate of 5/75 they will finish in 75/5 = 15 days.

How come this isn't correct?
Intern
Joined: 03 Jul 2015
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Location: India
Re: If 20% of certain quantity of work is done by A and the rest by B,  [#permalink]

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26 Apr 2019, 11:06
Because A & B are not working simultaneously in given situations. So assuming that B took 20 days to finish 80% of the work is wrong because B would have worked lesser number of days than that and same is true with A. You can assume it like B started the work, left it at some point and immediately A took over.

pourts wrote:
Would anyone be willing to explain why my method didn't work, and why I got a wrong answer?

Eq #1: 0.8 = B *20
Eq #3: 0.8 = A* 30

Solve Eq #1: B = 1/25 = 3/75 using 75 as a common denominator
Solve Eq #2: A = 2/75

Combined rate is 5/75. At a rate of 5/75 they will finish in 75/5 = 15 days.

How come this isn't correct?
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Posts: 1076
Location: United States
Re: If 20% of certain quantity of work is done by A and the rest by B,  [#permalink]

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09 Nov 2019, 08:08
Mohammed22Abrar wrote:
If 20% of certain quantity of work is done by A and 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

rate•time=work

1/5/a+4/5/b=20…1/5a+4/5b=20…b+4a/25ab=20
4/5/a+1/5/b=30…4/5a+1/5b=30…4b+a/25ab=30
4b+a/30=b+4a/20…80b+20a=30b+120a…b=2a
1/5a+4/5b=20…1/5a+4/5(2a)=20…a=3/100
t=1/a+b…t=1/a+2a…t=1/3a…t=1/3(3/100)
t=11+1/9

Ans (A)
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If 20% of certain quantity of work is done by A and the rest by B,  [#permalink]

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14 Nov 2019, 11:59
Mohammed22Abrar wrote:
If 20% of certain quantity of work is done by A and 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.

Hi Karishma,
I think in the last step, it should be 3/50 + 3/100 instead of 3/40+3/100. Please check.
A. 11 1/9
B. 10 1/9
C. 12
D. 15

Source: TIME material.

Use algebra:

0.2/A + 0.8/B = 20
1/A + 4/B = 100

0.8/A + 0.2/B = 30
4/A+ 1/B = 150

15/B = 250
B = 3/50 work per day
A = 3/100 work per day

Combined rate = 3/40 + 3/100 = 9/100
Time taken when working together = 100/9 = 11(1/9) days

It is not a GMAT type question. For GMAT, it's best to stick to GMAT material.

Hi Karishma,
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Posts: 677
Re: If 20% of certain quantity of work is done by A and the rest by B,  [#permalink]

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30 Nov 2019, 22:09
Could you tell me where I am wrong.

I wrote equations like this.

1/5a + 4/5b = 1/20
4/5a + 1/5b = 1/30

I add up both equations and got
1/a + 1/b = 50/600

Here I got A and B did the job in 12 days.

How I did it wrong!
Re: If 20% of certain quantity of work is done by A and the rest by B,   [#permalink] 30 Nov 2019, 22:09
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