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CAT Previous Year Paper | CAT Work and Time Questions | Question 22

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Question 22 : 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?

12
14.5
13.5
11

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Explanatory Answer

Method of solving this CAT Question from Work and Time

CAT 2018 Question Paper Quants Slot 2 Work and Time

Given that 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%.
To the original schedule of 16 days there are 9 more days and in this 9 days Ramesh fall short by 9 × 0.3x = 2.7x where x is the work done by Ramesh in a day
So the change = 2.7x (i.e. the gap because of drop in efficiency)
This 2.7x is compensated by one day of Ganesh + another 0.7 of Ramesh
2.7x = G + 0.7 x (Because the last day also he works with reduced efficiency)
2x = G
Hence Ganesh works twice as that of Ramesh.
If Ganesh had worked alone after Ramesh got sick means in the 7 days Ramesh would have completed \\frac{7}{48}) of the task
Ganesh on each day can do \\frac{1}{24}) of the task
Task to be completed by Ganesh is \\frac{41}{48}) completely
One day he can complete \\frac{1}{24}) so \\frac{41}{48}) × \\frac{24}{1}) = 20.5 days
If Ganesh had worked alone after Ramesh got sick, the no.of days needed for completing the remaining work is 20.5 – 7 = 13.5 days

The question is "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?"