CAT 2018 Slot 2 - QUANT Question 30

Question 30

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?

Solution

Let 'R' and 'G' be the amount of work that Ramesh and Ganesh can complete in a day. 

It is given that they can together complete a work in 16 days. Hence, total amount of work = 16(R+G) ... (1)

For first 7 days both of them worked together. From 8th day, Ramesh worked at 70% of his original efficiency whereas Ganesh worked at his original efficiency. It took them 17 days to finish the same work. i.e. Ramesh worked at 70% of his original efficiency for 10 days.

$$\Rightarrow$$ 16(R+G) = 7(R+G)+10(0.7R+G)

$$\Rightarrow$$ 16(R+G) = 14R+17G

$$\Rightarrow$$ R = 0.5G ... (2)

Total amount of work left when Ramesh got sick = 16(R+G) - 7(R+G) = 9(R+G) = 9(0.5+G) = 13.5G

Therefore, time taken by Ganesh to complete the remaining work = $$\dfrac{13.5G}{G}$$ = 13.5 days.


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