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
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