Questions from **Work and Time** have a lot of variety, making it slightly difficult with regards to Arithmetic. However, many such questions from **CAT Previous Year Paper**

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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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?"**

Choice C is the correct answer.

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