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

Question

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

A 12
B 14.5
C 13.5
D 11
E 9

nick1816 · Accepted Answer

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

GMATMBA5 · Answer

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

Kudos if helpful!

sharathnair14 · Answer

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

GMATGuruNY · Answer

Let the job = 480 widgets.

Ramesh and Ganesh can together complete a work in 16 days. 
Since Ramesh and Ganesh take 16 days to complete the 480-widget job, the rate for Ramesh and Ganesh together =  \frac{work}{time} = \frac{480}{16} = 30  widgets per day.

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. 
Since their combined rate = 30 widgets per day, the work produced by Ramesh and Ganesh in the first 7 days = rate*time = 30*7 = 210 widgets.
Since the remaining 270 widgets of the 480-widget job are produced in the last 10 days, the rate for the last 10 days =  \frac{work}{time} = \frac{270}{10} = 27  widgets per day.
Since the rate decreases from 30 widgets per day to 27 widgets per day -- and this decrease of 3 widgets per day represents 30% of Ramesh's rate -- we get:
 \frac{3}{10}R = 3 
R = 10 widgets per day
G = (combined rate for R and G) - (R's rate alone) = 30-10 = 20 widgets per day

If Ganesh had worked alone after Ramesh got sick, in how many days would he have completed the remaining work? 
Since Ganesh produces 20 widgets per day, the time for Ganesh to produced the remaining 270 widgets after the first 7 days  = \frac{work}{rate} = \frac{270}{20} = 13.5  days

C

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

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