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Minhaz and Alam can complete a work in 18 days...

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ShahadatHJ
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Minhaz and Alam can complete a work in 18 days... [#permalink] New post   12 Sep 2021, 07:52
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Minhaz and Alam can complete a work in 18 days. After working together for 12 days Minhaz stops, and Alam completes the remaining work in 8 days. In how many days can Mihaz complete the work if he works alone?

A. 32
B. 48
C. 56
D. 72
E. None of these
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D
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Re: Minhaz and Alam can complete a work in 18 days... [#permalink] New post   12 Sep 2021, 08:40
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ShahadatHJ wrote:
Minhaz and Alam can complete a work in 18 days. After working together for 12 days Minhaz stops, and Alam completes the remaining work in 8 days. In how many days can Mihaz complete the work if he works alone?

A. 32
B. 48
C. 56
D. 72
E. None of these



A way avoiding one hour work etc

In 12 hours, both will finish 12/18 or 2/3 work.

So, A finishes 1/3 in 20-12 or 8 days. This means A will finish entire work in 8*3 or 24 days.

Now A works for 20-18 or 2 days extra, while M works for 18-12 or 6 days less. This means 2 days of A is equal to 6 days of M.
So, M takes 24*3 or 72 days.


One day work.

\(\frac{18}{A}+\frac{18}{M}=\frac{12}{M}+\frac{20}{A}\)

\(\frac{2}{A}=\frac{6}{M}\)

\(M=3A\)

Thus, \(\frac{1}{A}+\frac{1}{M}=\frac{1}{18}\)

\(\frac{1}{A}+\frac{1}{3A}=\frac{1}{18}\)

\(\frac{4}{3A}=\frac{1}{18}\)

\(A=24…..M=24*3=72\)


D
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Re: Minhaz and Alam can complete a work in 18 days... [#permalink] New post   12 Sep 2021, 09:36
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let rate of Minhaz be x and that of Alam be y
given
x+y/x*y = 1/18
total days work 12 days
work done = 12*1/18 ; 2/3
work left ; 1/3
now Alam completes a/3 in 8 days ; rate of Alam = 24
x+24/24x= 1/18
solve for x = 72
option D
ShahadatHJ wrote:
Minhaz and Alam can complete a work in 18 days. After working together for 12 days Minhaz stops, and Alam completes the remaining work in 8 days. In how many days can Mihaz complete the work if he works alone?

A. 32
B. 48
C. 56
D. 72
E. None of these
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Re: Minhaz and Alam can complete a work in 18 days... [#permalink] New post   26 Sep 2021, 05:53
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ShahadatHJ wrote:
Minhaz and Alam can complete a work in 18 days. After working together for 12 days Minhaz stops, and Alam completes the remaining work in 8 days. In how many days can Mihaz complete the work if he works alone?

A. 32
B. 48
C. 56
D. 72
E. None of these

In 18 days, they can finish the entire work or 1.
So, in 12 days they can do 12/18 = 2/3 part of the entire work.
The remaining (1-(2/3))=1/3 part is done by Alam by 8 days.
Alam can do the entire work in 8*3 = 24 days.

Say, Minhaz can do the work in \(X\) days.
Now,
\(\frac{1}{24}\)+\(\frac{1}{X}\)=\(\frac{1}{18}\)
\(X\)=\(72\)

In such questions, the organization of data before forming an equation makes solving easier.

Ans. D
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Re: Minhaz and Alam can complete a work in 18 days... [#permalink] New post   09 Jan 2024, 08:21
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ShahadatHJ wrote:
Minhaz and Alam can complete a work in 18 days. After working together for 12 days Minhaz stops, and Alam completes the remaining work in 8 days. In how many days can Mihaz complete the work if he works alone?

A. 32
B. 48
C. 56
D. 72
E. None of these

Let the total work be 72 Units

Efficiency of Minhaz and Alam is 4

Work done by Minhaz and Alam in 12 days is 48 Units, 24 units of work is left...

Alam completes the remaining 24 units of work in 8 days.

So, Efficiency of Alam is 3 and thus efficiency of Minhaz is 1

Thus, Mihaz can complete the work in 72 days, Answer must be (D)
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Re: Minhaz and Alam can complete a work in 18 days... [#permalink] New post   12 Sep 2021, 10:31
ShahadatHJ wrote:
Minhaz and Alam can complete a work in 18 days. After working together for 12 days Minhaz stops, and Alam completes the remaining work in 8 days. In how many days can Mihaz complete the work if he works alone?

A. 32
B. 48
C. 56
D. 72
E. None of these


1/A + 1/M =1/18 .......2

12*( 1/A +1/M ) + 8*1/A = 1 .........1

substituing 2 in 1 and solving we get A =24........3

substituting 3 in 2 we get M =48
Therefore IMO D
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Re: Minhaz and Alam can complete a work in 18 days... [#permalink]
12 Sep 2021, 10:31
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