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 be have completed the remaining work?

Let R and G be daily work rates. R+G = 1/16. In 7 days, they do 7/16 work. Remaining work = 9/16. After 7 days, R's rate becomes 0.7R. They finish in 10 more days (17-7). So, 10(0.7R + G) = 9/16. 7R + 10G = 9/16. Solving the system: R+G=1/16 => 7R+7G=7/16. Subtracting gives 3G = 2/16, so G = 2/48 = 1/24. Remaining work 9/16 divided by G (1/24) = (9/16) * 24 = 216/16 = 13.5 days.