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Ramesh and Ganesh can together complete a work in 16 days.

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Ramesh and Ganesh can together complete a work in 16 days.  [#permalink]

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New post 23 Aug 2019, 11:02
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Ramesh and Ganesh can together complete a work in 16 days. After seven days of working together, Ramesh got sick and his efficiency fell by 30%. As a result, they completed the work in 17 days instead of 16 days. If Ganesh had worked alone after Ramesh got sick, in how many days would he have completed the remaining work?

A 12
B 14.5
C 13.5
D 11
E 9
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Re: Ramesh and Ganesh can together complete a work in 16 days.  [#permalink]

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New post 23 Aug 2019, 13:24
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Let efficiency of Ganesh= G
and efficiency of Ramesh= R

The work that both can finish in 16-7=9 days got finished in 16-6=10 days, because Ramesh efficiency reduced to 70%.

9(R+G)=10(0.7R+G)
9R+9G=7R+10G
G=2R

Number of days taken by Ganesh to complete the remaining work alone= \(\frac{9(R+G)}{G}\)= \(\frac{9*(0.5G+G)}{G}\)= 27/2=13.5



AbdulMalikVT wrote:
Ramesh and Ganesh can together complete a work in 16 days. After seven days of working together, Ramesh got sick and his efficiency fell by 30%. As a result, they completed the work in 17 days instead of 16 days. If Ganesh had worked alone after Ramesh got sick, in how many days would he have completed the remaining work?

A 12
B 14.5
C 13.5
D 11
E 9
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Re: Ramesh and Ganesh can together complete a work in 16 days.  [#permalink]

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New post 25 Aug 2019, 04:09
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Let \(R\) be the efficiency/rate of Ramesh
And, Let \(G\) be the efficiency of Ganesh

The work can be done in 16 days provided that \(R\) and \(G\)are simultaneous.

The work is done for the first 7 days at a rate of \(R+G\)
From the question, we understand that we need to find out the remaining work done.

The remaining work done will be \(9(R+G)\) ----- Let this be eqn 1

We know that \(9(R+G)=10(0.7R+G)\) from the given information.
\(=>\) \(9+9G=7R+10G\)
\(=> G=2R\) ----- Let this be eqn 2

The number of days for Ganesh to finish the work would be
\(Time = \frac{Work}{Rate}\)

From eqn 1 we know the work done wil be \(= 9(R+G)\)
And from eqn 2 we know that \(=> G=2R\)

\(=> \frac{9(R+G)}{G}\)
\(=>\frac{9(0.5G+G)}{G}\)
\(=> \frac{13.5G}{G}\)
\(=> 13.5 Days\)
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Re: Ramesh and Ganesh can together complete a work in 16 days.  [#permalink]

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New post 25 Aug 2019, 05:08
1
R = Rate of Ramesh; G = Rate of Ganesh; W1 = work done in first 7 days; W2 = work done in next 10 days; Wt = total work

Ramesh and Ganesh can complete the work normally in 16 days.
1 = (R+G)*16 _______(1)

Also, Wt = (R+G)*16__(2)

In first 7 days, work done W1 is,
w1 = (R+G)*7

In next 10 days, w2 is,
w2 = (0.7R+G)*10

Since w1 + w2 = wt
7R+7G+7R+10G=16R+16G
G=2R________(3)

From (1) & (3) we get,
R=1/48 and G=1/24
Therefore, w1 = 7/16 and w2 = 9/16

Time taken to complete remaining work if only Ganesh would have worked after 7 days -
w2=G*t
9/16=(1/24)*t
t=27/2 = 13.5

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Re: Ramesh and Ganesh can together complete a work in 16 days.   [#permalink] 25 Aug 2019, 05:08
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Ramesh and Ganesh can together complete a work in 16 days.

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